# 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.

## Answer and Explanation:

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}

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Understanding Concavity and Inflection Points with Differentiation

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