What is the derivative of cos^2(4pix) ?

The derivative of cos^2(4pix) is -8picos(4pix)sin(4pix)

What is the first derivative of cos^2(4pix) ?

The first derivative of cos^2(4pix) is -8picos(4pix)sin(4pix)

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\frac{d}{d x} (cos^{2} (4 π x))

- 8 π cos (4 π x) sin (4 π x)

Solution steps

\frac{d}{d x} (cos^{2} (4 π x))

Apply the chain rule:

2 cos (4 π x) \frac{d}{d x} (cos (4 π x))

= 2 cos (4 π x) \frac{d}{d x} (cos (4 π x))

\frac{d}{d x} (cos (4 π x)) = - sin (4 π x) \cdot 4 π

= 2 cos (4 π x) (- sin (4 π x) \cdot 4 π)

Simplify

= - 8 π cos (4 π x) sin (4 π x)

\int sec^{2} (2 x) tan^{2} (2 x) d x

x \to π lim (\frac{x}{4} - \frac{π}{2})

\int \frac{s ^{2}}{s ^{3} + 5} d s

\int_{0}^{1} 2 x^{2} d x

\int \frac{1}{x ^{2} - 2 x - 8} d x

What is the derivative of cos^2(4pix) ?
The derivative of cos^2(4pix) is -8picos(4pix)sin(4pix)
What is the first derivative of cos^2(4pix) ?
The first derivative of cos^2(4pix) is -8picos(4pix)sin(4pix)