What is the derivative of sin^4(2xcos^4(3x)) ?

The derivative of sin^4(2xcos^4(3x)) is 8cos^4(3x)sin^3(2x)cos(2x)-12sin^4(2x)cos^3(3x)sin(3x)

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

The first derivative of sin^4(2xcos^4(3x)) is 8cos^4(3x)sin^3(2x)cos(2x)-12sin^4(2x)cos^3(3x)sin(3x)

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\frac{d}{d x} (sin^{4} (2 x) cos^{4} (3 x))

8 cos^{4} (3 x) sin^{3} (2 x) cos (2 x) - 12 sin^{4} (2 x) cos^{3} (3 x) sin (3 x)

Solution steps

\frac{d}{d x} (sin^{4} (2 x) cos^{4} (3 x))

Apply the Product Rule:

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

f = sin^{4} (2 x), g = cos^{4} (3 x)

= \frac{d}{d x} (sin^{4} (2 x)) cos^{4} (3 x) + \frac{d}{d x} (cos^{4} (3 x)) sin^{4} (2 x)

\frac{d}{d x} (sin^{4} (2 x)) = 8 sin^{3} (2 x) cos (2 x)

\frac{d}{d x} (cos^{4} (3 x)) = - 12 cos^{3} (3 x) sin (3 x)

= 8 sin^{3} (2 x) cos (2 x) cos^{4} (3 x) + (- 12 cos^{3} (3 x) sin (3 x)) sin^{4} (2 x)

Simplify

= 8 cos^{4} (3 x) sin^{3} (2 x) cos (2 x) - 12 sin^{4} (2 x) cos^{3} (3 x) sin (3 x)

\frac{384 x}{x ^{2} + 289}

2 x^{2} + 3 x

\int_{0}^{1.2} (1 - \frac{y}{2}) d y

\frac{d}{d x} (\frac{u}{x})

x \to \infty lim (x^{x})

What is the derivative of sin^4(2xcos^4(3x)) ?
The derivative of sin^4(2xcos^4(3x)) is 8cos^4(3x)sin^3(2x)cos(2x)-12sin^4(2x)cos^3(3x)sin(3x)
What is the first derivative of sin^4(2xcos^4(3x)) ?
The first derivative of sin^4(2xcos^4(3x)) is 8cos^4(3x)sin^3(2x)cos(2x)-12sin^4(2x)cos^3(3x)sin(3x)