What is the derivative of sin^7(cos(5x)) ?

The derivative of sin^7(cos(5x)) is -35sin^6(cos(5x))cos(cos(5x))sin(5x)

What is the first derivative of sin^7(cos(5x)) ?

The first derivative of sin^7(cos(5x)) is -35sin^6(cos(5x))cos(cos(5x))sin(5x)

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derivative of

sin^{7} (cos (5 x))

- 35 sin^{6} (cos (5 x)) cos (cos (5 x)) sin (5 x)

Solution steps

\frac{d}{d x} (sin^{7} (cos (5 x)))

Apply the chain rule:

7 (sin (cos (5 x)))^{6} \frac{d}{d x} (sin (cos (5 x)))

= 7 (sin (cos (5 x)))^{6} \frac{d}{d x} (sin (cos (5 x)))

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

= 7 (sin (cos (5 x)))^{6} (- 5 cos (cos (5 x)) sin (5 x))

Simplify

= - 35 sin^{6} (cos (5 x)) cos (cos (5 x)) sin (5 x)

f (x) = 3 x^{2} + 2 x, at x = - 3

\frac{\partial}{\partial y} ((e^{x} - x) cos (y))

\int (sin (x) - 5 cos (x)) d x

x \to 1 lim (\frac{x}{x ^{2} + 1})

\frac{\partial}{\partial x} (e^{- 2 x^{2} - 5 y^{2}})

What is the derivative of sin^7(cos(5x)) ?
The derivative of sin^7(cos(5x)) is -35sin^6(cos(5x))cos(cos(5x))sin(5x)
What is the first derivative of sin^7(cos(5x)) ?
The first derivative of sin^7(cos(5x)) is -35sin^6(cos(5x))cos(cos(5x))sin(5x)