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

The answer to (\partial)/(\partial x)(5cos(5x)) is -25sin(5x)

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

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

- 25 sin (5 x)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

- sin (5 x) \frac{\partial}{\partial x} (5 x)

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

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

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

Simplify

= - 25 sin (5 x)

What is (\partial)/(\partial x)(5cos(5x)) ?
The answer to (\partial)/(\partial x)(5cos(5x)) is -25sin(5x)