Question

Differentiate the function. f(x) = sin(9 ln(x))

Answer 1

Answer: $f'(x)=\dfrac{9\cos(9\ln (x))}{x}$.

Step-by-step explanation:

The given function is

$f(x)=\sin(9\ln (x))$

Using chain rule differentiate w.r.t. x.

$f'(x)=\cos(9\ln (x))\dfrac{d}{dx}(9\ln (x))$      $\left[\because \dfrac{d}{dx}\sin x=\cos x\right]$

$f'(x)=\cos(9\ln (x))\left[9\dfrac{d}{dx}(\ln (x))\right]$

$f'(x)=\cos(9\ln (x))\left[9\times \dfrac{1}{x}\right]$       $\left[\because \dfrac{d}{dx}\ln x=\dfrac{1}{x}\right]$

$f'(x)=\dfrac{9\cos(9\ln (x))}{x}$

Therefore, $f'(x)=\dfrac{9\cos(9\ln (x))}{x}$.