# Find the second derivative of the function f(x)=\cos ^{2}x-2\sin x.

## Question:

Find the second derivative of the function {eq}\displaystyle f(x)=\cos ^{2}x-2\sin x. {/eq}

## Second derivative:

To find the second derivative we will double differentiate the function after differentiating one time we will rearrange the expression suing trigonometric identity and then again differentiate.

To find the derivative we will differentiate the function:

{eq}f(x)=\cos ^{2}x-2\sin x {/eq}

After differentiating it we get:

{eq}f'(x)=-2\cos x\sin x-2\cos x\\ =-\sin 2x-2\cos x {/eq}

Again differentiating we get:

{eq}f''(x)=-2\cos 2x+2\sin x {/eq}