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Popular >

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

Solution

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

Solution

4 sin^{3} (x) cos (x)

Solution steps

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

Simplify

(sin^{2} (x))^{2} : sin^{4} (x)

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

Apply the chain rule:

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

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

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

= 4 (sin (x))^{3} cos (x)

Simplify

= 4 sin^{3} (x) cos (x)

Popular Examples

integral of sin(6x)cos(2x)

\int sin (6 x) cos (2 x) d x

integral of cos^4(7-x)sin(7-x)

\int cos^{4} (7 - x) sin (7 - x) d x

(dy)/(dx)=e^{3y}sin(4x)

\frac{d y}{d x} = e^{3 y} sin (4 x)

sum from n=0 to infinity of 1/(n^2+2n)

n = 0 \sum \infty \frac{1}{n ^{2} + 2 n}

integral of (5000x)/(25x+1500)

\int \frac{5000 x}{25 x + 1500} d x

Frequently Asked Questions (FAQ)

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