{"id":4285,"date":"2022-06-11T06:06:07","date_gmt":"2022-06-11T06:06:07","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=4285"},"modified":"2022-06-11T06:06:07","modified_gmt":"2022-06-11T06:06:07","slug":"how-to-find-the-derivatives","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/06\/11\/how-to-find-the-derivatives\/","title":{"rendered":"How To Find The Derivatives?"},"content":{"rendered":"\n<p>Derivatives are obtained by applying the&nbsp;limits&nbsp;as per the first principle of differentiation that we obtained as the definition of a derivative. Let f(x) = 4x<sup>2&nbsp;<\/sup>+ 3<\/p>\n\n\n\n<p>f\u2032(x)=lim <sub>\u03b4x\u21920<\/sub>  f(x+\u03b4x) \u2212 f(x)  \/ \u03b4x<\/p>\n\n\n\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n  <msup>\n    <mi>f<\/mi>\n    <mo>\u2032<\/mo>\n  <\/msup>\n  <mo stretchy=\"false\">(<\/mo>\n  <mi>x<\/mi>\n  <mo stretchy=\"false\">)<\/mo>\n  <mo>=<\/mo>\n  <munder>\n    <mo movablelimits=\"true\" form=\"prefix\">lim<\/mo>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mi>\u03b4<!-- \u03b4 --><\/mi>\n      <mi>x<\/mi>\n      <mo stretchy=\"false\">\u2192<!-- \u2192 --><\/mo>\n      <mn>0<\/mn>\n    <\/mrow>\n  <\/munder>\n  <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n    <mfrac>\n      <mrow>\n        <mi>f<\/mi>\n        <mo stretchy=\"false\">(<\/mo>\n        <mi>x<\/mi>\n        <mo>+<\/mo>\n        <mi>\u03b4<!-- \u03b4 --><\/mi>\n        <mi>x<\/mi>\n        <mo stretchy=\"false\">)<\/mo>\n        <mo>\u2212<!-- \u2212 --><\/mo>\n        <mi>f<\/mi>\n        <mo stretchy=\"false\">(<\/mo>\n        <mi>x<\/mi>\n        <mo stretchy=\"false\">)<\/mo>\n      <\/mrow>\n      <mrow>\n        <mi>\u03b4<!-- \u03b4 --><\/mi>\n        <mi>x<\/mi>\n      <\/mrow>\n    <\/mfrac>\n  <\/mstyle>\n  <mspace linebreak=\"newline\"><\/mspace>\n  <mo>=<\/mo>\n  <munder>\n    <mo movablelimits=\"true\" form=\"prefix\">lim<\/mo>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mi>\u03b4<!-- \u03b4 --><\/mi>\n      <mi>x<\/mi>\n      <mo stretchy=\"false\">\u2192<!-- \u2192 --><\/mo>\n      <mn>0<\/mn>\n    <\/mrow>\n  <\/munder>\n  <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n    <mfrac>\n      <mrow>\n        <mo stretchy=\"false\">(<\/mo>\n        <mn>4<\/mn>\n        <mo stretchy=\"false\">(<\/mo>\n        <mi>x<\/mi>\n        <mo>+<\/mo>\n        <mi>\u03b4<!-- \u03b4 --><\/mi>\n        <mi>x<\/mi>\n        <msup>\n          <mo stretchy=\"false\">)<\/mo>\n          <mn>2<\/mn>\n        <\/msup>\n        <mo>+<\/mo>\n        <mn>3<\/mn>\n        <mo stretchy=\"false\">)<\/mo>\n        <mo>\u2212<!-- \u2212 --><\/mo>\n        <mo stretchy=\"false\">(<\/mo>\n        <mn>4<\/mn>\n        <msup>\n          <mi>x<\/mi>\n          <mn>2<\/mn>\n        <\/msup>\n        <mo>+<\/mo>\n        <mn>3<\/mn>\n        <mo stretchy=\"false\">)<\/mo>\n      <\/mrow>\n      <mrow>\n        <mi>\u03b4<!-- \u03b4 --><\/mi>\n        <mi>x<\/mi>\n      <\/mrow>\n    <\/mfrac>\n  <\/mstyle>\n  <mspace linebreak=\"newline\"><\/mspace>\n  <mo>=<\/mo>\n  <munder>\n    <mo movablelimits=\"true\" form=\"prefix\">lim<\/mo>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mi>\u03b4<!-- \u03b4 --><\/mi>\n      <mi>x<\/mi>\n      <mo stretchy=\"false\">\u2192<!-- \u2192 --><\/mo>\n      <mn>0<\/mn>\n    <\/mrow>\n  <\/munder>\n  <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n    <mfrac>\n      <mrow>\n        <mo stretchy=\"false\">(<\/mo>\n        <mn>4<\/mn>\n        <msup>\n          <mi>x<\/mi>\n          <mn>2<\/mn>\n        <\/msup>\n        <mo>+<\/mo>\n        <mn>4<\/mn>\n        <mi>\u03b4<!-- \u03b4 --><\/mi>\n        <msup>\n          <mi>x<\/mi>\n          <mn>2<\/mn>\n        <\/msup>\n        <mo>+<\/mo>\n        <mn>8<\/mn>\n        <mi>x<\/mi>\n        <mi>\u03b4<!-- \u03b4 --><\/mi>\n        <mi>x<\/mi>\n        <mo>+<\/mo>\n        <mn>3<\/mn>\n        <mo stretchy=\"false\">)<\/mo>\n        <mo>\u2212<!-- \u2212 --><\/mo>\n        <mo stretchy=\"false\">(<\/mo>\n        <mn>4<\/mn>\n        <msup>\n          <mi>x<\/mi>\n          <mn>2<\/mn>\n        <\/msup>\n        <mo>+<\/mo>\n        <mn>3<\/mn>\n        <mo stretchy=\"false\">)<\/mo>\n      <\/mrow>\n      <mrow>\n        <mi>\u03b4<!-- \u03b4 --><\/mi>\n        <mi>x<\/mi>\n      <\/mrow>\n    <\/mfrac>\n  <\/mstyle>\n  <mspace linebreak=\"newline\"><\/mspace>\n  <mo>=<\/mo>\n  <munder>\n    <mo movablelimits=\"true\" form=\"prefix\">lim<\/mo>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mi>\u03b4<!-- \u03b4 --><\/mi>\n      <mi>x<\/mi>\n      <mo stretchy=\"false\">\u2192<!-- \u2192 --><\/mo>\n      <mn>0<\/mn>\n    <\/mrow>\n  <\/munder>\n  <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n    <mfrac>\n      <mrow>\n        <mo stretchy=\"false\">(<\/mo>\n        <mn>4<\/mn>\n        <msup>\n          <mi>x<\/mi>\n          <mn>2<\/mn>\n        <\/msup>\n        <mo>+<\/mo>\n        <mn>4<\/mn>\n        <mi>\u03b4<!-- \u03b4 --><\/mi>\n        <msup>\n          <mi>x<\/mi>\n          <mn>2<\/mn>\n        <\/msup>\n        <mo>+<\/mo>\n        <mn>8<\/mn>\n        <mi>x<\/mi>\n        <mi>\u03b4<!-- \u03b4 --><\/mi>\n        <mi>x<\/mi>\n        <mo>+<\/mo>\n        <mn>3<\/mn>\n        <mo>\u2212<!-- \u2212 --><\/mo>\n        <mn>4<\/mn>\n        <msup>\n          <mi>x<\/mi>\n          <mn>2<\/mn>\n        <\/msup>\n        <mo>\u2212<!-- \u2212 --><\/mo>\n        <mn>3<\/mn>\n        <mo stretchy=\"false\">)<\/mo>\n      <\/mrow>\n      <mrow>\n        <mi>\u03b4<!-- \u03b4 --><\/mi>\n        <mi>x<\/mi>\n      <\/mrow>\n    <\/mfrac>\n  <\/mstyle>\n  <mspace linebreak=\"newline\"><\/mspace>\n  <mo>=<\/mo>\n  <munder>\n    <mo movablelimits=\"true\" form=\"prefix\">lim<\/mo>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mi>\u03b4<!-- \u03b4 --><\/mi>\n      <mi>x<\/mi>\n      <mo stretchy=\"false\">\u2192<!-- \u2192 --><\/mo>\n      <mn>0<\/mn>\n    <\/mrow>\n  <\/munder>\n  <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n    <mfrac>\n      <mrow>\n        <mn>4<\/mn>\n        <mi>\u03b4<!-- \u03b4 --><\/mi>\n        <msup>\n          <mi>x<\/mi>\n          <mn>2<\/mn>\n        <\/msup>\n        <mo>+<\/mo>\n        <mn>8<\/mn>\n        <mi>x<\/mi>\n        <mi>\u03b4<!-- \u03b4 --><\/mi>\n        <mi>x<\/mi>\n      <\/mrow>\n      <mrow>\n        <mi>\u03b4<!-- \u03b4 --><\/mi>\n        <mi>x<\/mi>\n      <\/mrow>\n    <\/mfrac>\n  <\/mstyle>\n  <mspace linebreak=\"newline\"><\/mspace>\n  <mo>=<\/mo>\n  <munder>\n    <mo movablelimits=\"true\" form=\"prefix\">lim<\/mo>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mi>\u03b4<!-- \u03b4 --><\/mi>\n      <mi>x<\/mi>\n      <mo stretchy=\"false\">\u2192<!-- \u2192 --><\/mo>\n      <mn>0<\/mn>\n    <\/mrow>\n  <\/munder>\n  <mn>4<\/mn>\n  <mi>\u03b4<!-- \u03b4 --><\/mi>\n  <mi>x<\/mi>\n  <mo>+<\/mo>\n  <mn>8<\/mn>\n  <mi>x<\/mi>\n<\/math>\n\n\n\n<p>Therefore the first derivative of 4x<sup>2<\/sup>&nbsp;+ 3 = 8x.<\/p>\n\n\n\n<p>Thus the first derivative of an algebraic function is derived using the definition of the derivative.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Derivatives are obtained by applying the&nbsp;limits&nbsp;as per the first principle of differentiation that we obtained as the definition of a derivative. Let f(x) = 4&#215;2&nbsp;+ 3 f\u2032(x)=lim \u03b4x\u21920 f(x+\u03b4x) \u2212 f(x) \/ \u03b4x f \u2032 ( x ) = lim \u03b4 x \u2192 0 f ( x + \u03b4 x ) \u2212 f ( x [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[799],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4285"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=4285"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4285\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=4285"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=4285"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=4285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}