What is (\partial)/(\partial x)(cos^2(4pix)) ?

The answer to (\partial)/(\partial x)(cos^2(4pix)) is -8picos(4pix)sin(4pix)

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(\partial)/(\partial x)(cos^2(4pix))

\frac{\partial}{\partial x} (cos^{2} (4 π x))

- 8 π cos (4 π x) sin (4 π x)

Solution steps

\frac{\partial}{\partial x} (cos^{2} (4 π x))

Apply the chain rule:

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

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

\frac{\partial}{\partial 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)

\frac{d ^{2}}{d x ^{2}} (e^{- a x^{2}})

x \to \infty lim \frac{x}{x x x}

\int (- x^{2} + 6 x - 5) d x

\int \frac{x - 2}{3 x + 6} d x

\frac{d}{d x} (16 - x^{2} - y^{2})

What is (\partial)/(\partial x)(cos^2(4pix)) ?
The answer to (\partial)/(\partial x)(cos^2(4pix)) is -8picos(4pix)sin(4pix)