What is the derivative of sin^2(2xcos^3(3x)) ?

The derivative of sin^2(2xcos^3(3x)) is 2cos^3(3x)sin(4x)-9cos^2(3x)sin^2(2x)sin(3x)

What is the first derivative of sin^2(2xcos^3(3x)) ?

The first derivative of sin^2(2xcos^3(3x)) is 2cos^3(3x)sin(4x)-9cos^2(3x)sin^2(2x)sin(3x)

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

2 cos^{3} (3 x) sin (4 x) - 9 cos^{2} (3 x) sin^{2} (2 x) sin (3 x)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin^{2} (2 x), g = cos^{3} (3 x)

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

\frac{d}{d x} (sin^{2} (2 x)) = 2 sin (4 x)

\frac{d}{d x} (cos^{3} (3 x)) = - 9 cos^{2} (3 x) sin (3 x)

= 2 sin (4 x) cos^{3} (3 x) + (- 9 cos^{2} (3 x) sin (3 x)) sin^{2} (2 x)

Simplify

= 2 cos^{3} (3 x) sin (4 x) - 9 cos^{2} (3 x) sin^{2} (2 x) sin (3 x)

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\int \frac{x + 16}{x ^{2} + 2 x - 8} d x

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What is the derivative of sin^2(2xcos^3(3x)) ?
The derivative of sin^2(2xcos^3(3x)) is 2cos^3(3x)sin(4x)-9cos^2(3x)sin^2(2x)sin(3x)
What is the first derivative of sin^2(2xcos^3(3x)) ?
The first derivative of sin^2(2xcos^3(3x)) is 2cos^3(3x)sin(4x)-9cos^2(3x)sin^2(2x)sin(3x)