Difference between revisions of "Simplifying Derivatives"

Revision as of 14:58, 8 October 2021

$a'(x)=x^{3}{(2x-5)}^{4}$

Product Rule $(f*g)'=f*g'+g*f'$

$f=x^{3}$ $f'=3x^{2}$ $g={(2x-5)}^{4}$ $g'=4{(2x-5)}^{3}(2)$

$a'=(x^{3})(3x^{2})+({(2x-5)}^{4})(4{(2x-5)}^{3}(2))$

$f'(x)=x^{2}{\sqrt[{2}]{4-9x}}$ simplify

Chain rule $[f(g(x))]'=f'(g(x))*g'(x)$

$2x{\sqrt[{2}]{4-9x}}+{-9 \over 2}{(4-9x)}^{-1 \over 2}$

${x(8-{45x \over 2}){\sqrt[{2}]{4-9x}} \over {\sqrt[{2}]{4-9x}}}$

@@ Line 1: / Line 1: @@
 ====example 1====
-<math>f'(x)= x^2 \sqrt[2]{4-9x}</math>
+<math>a'(x)= x^3 {(2x-5)}^4</math>
+Product Rule <math>(f*g)'=f*g'+ g*f'</math>
+<math>f=x^3</math>
+<math>f'=3x^2</math>
+<math>g={(2x-5)}^4</math>
+<math>g'=4 {(2x-5)}^3 (2)</math>
+<math>a' = (x^3)(3x^2) + ({(2x-5)}^4)(4 {(2x-5)}^3 (2))</math>
 ====example 2====
 <math>f'(x)= x^2 \sqrt[2]{4-9x}</math> simplify