Question

find dy/dx y= cos^3[log(x^3)]​

Answer 1

${ \bold{ \boxed{ \boxed{ \mathtt { \red{\huge{ \bigstar \: ANSWER \: \bigstar}}}}}}}$

${ \bold{ \mathtt{ \orange{\: : \implies \: y = {cos}^{3}( log( {x}^{3} )) }}}} \\ \\ \\ { \bold{ \mathtt{ \orange{\: : \implies \frac{dy}{dx} = 3 {cos}^{2}( log( {x}^{3} ) )( - \sin( log( {x}^{3} ) ) ( \frac{1}{ {x}^{3} })(3 {x}^{2} ) }}}} \\ \\ \\ { \bold{ \mathtt{ \orange{\: : \implies \frac{dy}{dx} = - 9 {cos}^{2} ( log( {x}^{3} )) \sin( log( {x}^{3} ) ) ( \frac{1}{x} ) }}}} \\ \\ { \bold{ \mathtt{ \green{ \underline{ \underline{Used \: \: formula }} : - }}}} \\ \\ { \bold{ \pink{ \mathtt{(1) \: y = {x}^{n} \: \implies \: \frac{dy}{dx} = n {x}^{n - 1} }}}} \\ \\ { \bold{ \pink{ \mathtt{(2) \: y = \cos(x) \: \implies \: \frac{dy}{dx} = - \sin(x) }}}} \\ \\ { \bold{ \pink{ \mathtt{(3)y = log(x) \: \implies \: \frac{dy}{dx} = \frac{1}{x} }}}}$