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

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

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(\partial)/(\partial x)(-cos^2(x))

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

sin (2 x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

= - 2 cos (x) (- sin (x))

Simplify

- 2 cos (x) (- sin (x)) : sin (2 x)

= sin (2 x)

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