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

x y^{^{'}} + y = 40 x

\int \frac{sin ( x )}{7 + cos ( x )} d x

\frac{\partial}{\partial x} (y ln (x^{3} + y^{3} + 8) - 7)

\int y^{2} + 1 d y

\frac{d}{d x} ((5 + 3 x) cos (x))

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