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Popular >

derivative of cos(sin^3(5x-5))

Solution

\frac{d}{d x} (cos (sin^{3} (5 x - 5)))

Solution

- sin (sin^{3} (5 x - 5)) \cdot 15 sin^{2} (5 x - 5) cos (5 x - 5)

Solution steps

\frac{d}{d x} (cos (sin^{3} (5 x - 5)))

Apply the chain rule:

- sin (sin^{3} (5 x - 5)) \frac{d}{d x} (sin^{3} (5 x - 5))

= - sin (sin^{3} (5 x - 5)) \frac{d}{d x} (sin^{3} (5 x - 5))

\frac{d}{d x} (sin^{3} (5 x - 5)) = 15 sin^{2} (5 x - 5) cos (5 x - 5)

= - sin (sin^{3} (5 x - 5)) \cdot 15 sin^{2} (5 x - 5) cos (5 x - 5)

Popular Examples

y^'=((y^3+1))/((3xy^2))

y^{^{'}} = \frac{( y ^{3} + 1 )}{( 3 x y ^{2} )}

limit as x approaches+1 of (1-|x|)/(x-1)

x \to + 1 lim (\frac{1 - ∣ x ∣}{x - 1})

integral of (x^3)/(sqrt(1+x^4))

\int \frac{x ^{3}}{1 + x ^{4}} d x

y^{^{'}} - y + x^{2} = 0

integral from 3 to 6 of 1/(x^2-1)

\int_{3}^{6} \frac{1}{x ^{2} - 1} d x

Frequently Asked Questions (FAQ)

What is the derivative of cos(sin^3(5x-5)) ?
The derivative of cos(sin^3(5x-5)) is -sin(sin^3(5x-5))*15sin^2(5x-5)cos(5x-5)
What is the first derivative of cos(sin^3(5x-5)) ?
The first derivative of cos(sin^3(5x-5)) is -sin(sin^3(5x-5))*15sin^2(5x-5)cos(5x-5)