What is (\partial)/(\partial x)(cos^3(x)) ?

The answer to (\partial)/(\partial x)(cos^3(x)) is -3cos^2(x)sin(x)

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(\partial)/(\partial x)(cos^3(x))

\frac{\partial}{\partial x} (cos^{3} (x))

- 3 cos^{2} (x) sin (x)

Solution steps

\frac{\partial}{\partial x} (cos^{3} (x))

Apply the chain rule:

3 (cos (x))^{2} \frac{\partial}{\partial x} (cos (x))

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

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

= 3 (cos (x))^{2} (- sin (x))

Simplify

= - 3 cos^{2} (x) sin (x)

\int \frac{x + 16}{x} d x

x \to - 3 lim (- (3 x))

e^{(3 h^{2} + 6)}

t \to 0 lim (\frac{( e ^{t} - 1 )}{t})

\frac{d}{d x} ((x + y)^{2} + (x + 1)^{2})

What is (\partial)/(\partial x)(cos^3(x)) ?
The answer to (\partial)/(\partial x)(cos^3(x)) is -3cos^2(x)sin(x)