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

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

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

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

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derivative of

cos^{3} (π x)

- 3 π cos^{2} (π x) sin (π x)

Solution steps

\frac{d}{d x} (cos^{3} (π x))

Apply the chain rule:

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

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

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

= 3 (cos (π x))^{2} (- sin (π x) π)

Simplify

= - 3 π cos^{2} (π x) sin (π x)

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