Question

What is the derivative of f(x)= 3cos^2 (x)

Answer 1

The solution to the problem is as follows:

f(x) = 3cos^2(x)f'(x) = 3*2cos(x)*d(cos(x))/dxf'(x) = 6cos(x)*(-sin(x))f'(x) = -6sin(x)cos(x), since sin(2x) = 2sin(x)cos(x)f'(x) = -3sin(2x)

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Answer 2

$\large\begin{array}{l} \textsf{Finding the derivative of}\\\\ \mathsf{f(x)=3\,cos^2\,x} \end{array}$

$\large\begin{array}{l} \textsf{You can differentiate it using the chain rule}\\\\ \mathsf{f'(x)=(3\,cos^2\,x)'}\\\\ \mathsf{f'(x)=3\,(cos^2\,x)'}\\\\ \mathsf{f'(x)=3\cdot 2\,(cos\,x)^{2-1}\cdot (cos\,x)'}\\\\ \mathsf{f'(x)=6\,(cos\,x)^1\cdot (-sin\,x)}\\\\ \boxed{\begin{array}{c}\mathsf{f'(x)=-6\,cos\,x\,sin\,x} \end{array}}\qquad\checkmark \end{array}$


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Tags: derivative trig function cosine cos power chain rule differential calculus