What is (\partial)/(\partial x)(cos^n(x)) ?

The answer to (\partial)/(\partial x)(cos^n(x)) is -nsin(x)cos^{n-1}(x)

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(\partial)/(\partial x)(cos^n(x))

\frac{\partial}{\partial x} (cos^{n} (x))

- n sin (x) cos^{n - 1} (x)

Solution steps

\frac{\partial}{\partial x} (cos^{n} (x))

Apply the chain rule:

n (cos (x))^{n - 1} \frac{\partial}{\partial x} (cos (x))

= n (cos (x))^{n - 1} \frac{\partial}{\partial x} (cos (x))

\frac{\partial}{\partial x} (cos (x)) = - sin (x)

= n (cos (x))^{n - 1} (- sin (x))

Simplify

= - n sin (x) cos^{n - 1} (x)

\int_{0.5}^{1} \frac{4}{9} x (5 - x^{2}) d x

x \to 0 - lim (- 2 x^{2} + 2 x)

\int \frac{3}{x ( x - 3 ) ^{2}} d x

\int sec^{2} (y) d y

n = 1 \sum \infty (\frac{8}{9})^{n}

What is (\partial)/(\partial x)(cos^n(x)) ?
The answer to (\partial)/(\partial x)(cos^n(x)) is -nsin(x)cos^{n-1}(x)