Question

let ( h(x)=9cos(x)-7x^{2}). ( h(x)=square) worked example: derivatives of (sin(x)) and (cos(x)) related content

Explanation:

Step1: Recall derivative rules

The derivative of $\cos(x)$ is $-\sin(x)$ and the derivative of $x^n$ is $nx^{n - 1}$.

Step2: Differentiate each term

The derivative of $9\cos(x)$ is $9\times(-\sin(x))=- 9\sin(x)$ using the constant - multiple rule. The derivative of $-7x^{2}$ is $-7\times2x=-14x$ using the power rule.

Step3: Combine derivatives

By the sum - difference rule of derivatives, if $h(x)=u(x)+v(x)$ then $h'(x)=u'(x)+v'(x)$. Here $u(x)=9\cos(x)$ and $v(x)=-7x^{2}$, so $h'(x)=-9\sin(x)-14x$.

Answer:

$-9\sin(x)-14x$