What is the derivative of cos(sin(5x)) ?

The derivative of cos(sin(5x)) is -sin(sin(5x))cos(5x)*5

What is the first derivative of cos(sin(5x)) ?

The first derivative of cos(sin(5x)) is -sin(sin(5x))cos(5x)*5

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\frac{d}{d x} (cos (sin (5 x)))

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

Solution steps

\frac{d}{d x} (cos (sin (5 x)))

Apply the chain rule:

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

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

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

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

What is the derivative of cos(sin(5x)) ?
The derivative of cos(sin(5x)) is -sin(sin(5x))cos(5x)*5
What is the first derivative of cos(sin(5x)) ?
The first derivative of cos(sin(5x)) is -sin(sin(5x))cos(5x)*5