Question

let
$f(x)=6\cos(\cos x)$
$f(x)=$
question help: video message

Explanation:

Step1: Apply the chain rule

Let $u = \cos x$. Then $f(x)=6\cos(u)$. The derivative of $y = \cos(u)$ with respect to $u$ is $y^\prime=-\sin(u)$, and the derivative of $u=\cos x$ with respect to $x$ is $u^\prime=-\sin x$.

Step2: Use the chain - rule formula $f^\prime(x)=\frac{df}{du}\cdot\frac{du}{dx}$

We have $\frac{df}{du}=- 6\sin(u)$ and $\frac{du}{dx}=-\sin x$. Substituting $u = \cos x$ back in, we get $f^\prime(x)=-6\sin(\cos x)\cdot(-\sin x)$.

Step3: Simplify the expression

$f^\prime(x)=6\sin x\sin(\cos x)$

Answer:

$6\sin x\sin(\cos x)$