Find the 2nd Derivative f(x)=cos(x)

Problem

ƒ(x)=cos(x)

Solution

1. Identify the function to be differentiated, which is ƒ(x)=cos(x)

2. Find the first derivative by applying the basic trigonometric differentiation rule d(cos(x))/d(x)=−sin(x)

ƒ(x)′=−sin(x)

3. Find the second derivative by differentiating the first derivative with respect to x

ƒ(x)″=(d(−)*sin(x))/d(x)

4. Apply the rule for the derivative of the sine function, d(sin(x))/d(x)=cos(x) and keep the negative sign.

ƒ(x)″=−cos(x)

Final Answer

ƒ(x)″=−cos(x)

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