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Popular >

derivative of 5cos^2(pix)

Solution

\frac{d}{d x} (5 cos^{2} (π x))

Solution

- 10 π cos (π x) sin (π x)

Solution steps

\frac{d}{d x} (5 cos^{2} (π x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (cos^{2} (π x))

Apply the chain rule:

2 cos (π x) \frac{d}{d x} (cos (π x))

= 2 cos (π x) \frac{d}{d x} (cos (π x))

\frac{d}{d x} (cos (π x)) = - sin (π x) π

= 5 \cdot 2 cos (π x) (- sin (π x) π)

Simplify

= - 10 π cos (π x) sin (π x)

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Frequently Asked Questions (FAQ)

What is the derivative of 5cos^2(pix) ?
The derivative of 5cos^2(pix) is -10picos(pix)sin(pix)
What is the first derivative of 5cos^2(pix) ?
The first derivative of 5cos^2(pix) is -10picos(pix)sin(pix)