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Popular >

derivative of cos^3(sin(2x))

Solution

\frac{d}{d x} (cos^{3} (sin (2 x)))

Solution

- 6 cos^{2} (sin (2 x)) sin (sin (2 x)) cos (2 x)

Solution steps

\frac{d}{d x} (cos^{3} (sin (2 x)))

Apply the chain rule:

3 (cos (sin (2 x)))^{2} \frac{d}{d x} (cos (sin (2 x)))

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

\frac{d}{d x} (cos (sin (2 x))) = - sin (sin (2 x)) cos (2 x) \cdot 2

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

Simplify

= - 6 cos^{2} (sin (2 x)) sin (sin (2 x)) cos (2 x)

Popular Examples

factor 15x^4-4x^3 factor

15 x^{4} - 4 x^{3}

integral of 10x^{3/7}+7x^{-6/7}

\int 10 x^{\frac{3}{7}} + 7 x^{- \frac{6}{7}} d x

limit as x approaches 10 of x^2

x \to 10 lim (x^{2})

y^{''}+0.2121y^'+2y=cos(4x),y(0)=0

y^{^{''}} + 0.2121 y^{^{'}} + 2 y = cos (4 x), y (0) = 0

integral of ((ln(x^{15})))/x

\int \frac{( ln ( x ^{15} ) )}{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of cos^3(sin(2x)) ?
The derivative of cos^3(sin(2x)) is -6cos^2(sin(2x))sin(sin(2x))cos(2x)
What is the first derivative of cos^3(sin(2x)) ?
The first derivative of cos^3(sin(2x)) is -6cos^2(sin(2x))sin(sin(2x))cos(2x)