What is (\partial)/(\partial x)(cos^2(5x)) ?

The answer to (\partial)/(\partial x)(cos^2(5x)) is -5sin(10x)

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(\partial)/(\partial x)(cos^2(5x))

\frac{\partial}{\partial x} (cos^{2} (5 x))

- 5 sin (10 x)

Solution steps

\frac{\partial}{\partial x} (cos^{2} (5 x))

Apply the chain rule:

2 cos (5 x) \frac{\partial}{\partial x} (cos (5 x))

= 2 cos (5 x) \frac{\partial}{\partial x} (cos (5 x))

\frac{\partial}{\partial x} (cos (5 x)) = - sin (5 x) \cdot 5

= 2 cos (5 x) (- sin (5 x) \cdot 5)

Simplify

2 cos (5 x) (- sin (5 x) \cdot 5) : - 5 sin (10 x)

= - 5 sin (10 x)

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5 y^{^{''}} + y^{^{'}} = - 6 x, y (0) = 0, y^{^{'}} (0) = - 20

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What is (\partial)/(\partial x)(cos^2(5x)) ?
The answer to (\partial)/(\partial x)(cos^2(5x)) is -5sin(10x)