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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

Graph

Popular Examples

integral of 1/(25+x^2)

\int \frac{1}{25 + x ^{2}} d x

derivative of (x^2y^2/2-2xy-y^2)

\frac{d}{d x} (\frac{x ^{2} y ^{2}}{2} - 2 x y - y^{2})

(1 + y) d y = 2 t d t

integral of (x^2)/(sqrt(16-x^2))

\int \frac{x ^{2}}{16 - x ^{2}} d x

derivative of \sqrt[3]{1+x}derivative of

3 1 + x

Frequently Asked Questions (FAQ)

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