What is the derivative of cos^2(3pix) ?

The derivative of cos^2(3pix) is -6picos(3pix)sin(3pix)

What is the first derivative of cos^2(3pix) ?

The first derivative of cos^2(3pix) is -6picos(3pix)sin(3pix)

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\frac{d}{d x} (cos^{2} (3 π x))

- 6 π cos (3 π x) sin (3 π x)

Solution steps

\frac{d}{d x} (cos^{2} (3 π x))

Apply the chain rule:

2 cos (3 π x) \frac{d}{d x} (cos (3 π x))

= 2 cos (3 π x) \frac{d}{d x} (cos (3 π x))

\frac{d}{d x} (cos (3 π x)) = - sin (3 π x) \cdot 3 π

= 2 cos (3 π x) (- sin (3 π x) \cdot 3 π)

Simplify

= - 6 π cos (3 π x) sin (3 π x)

What is the derivative of cos^2(3pix) ?
The derivative of cos^2(3pix) is -6picos(3pix)sin(3pix)
What is the first derivative of cos^2(3pix) ?
The first derivative of cos^2(3pix) is -6picos(3pix)sin(3pix)