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Popular >

derivative of 1/4 sin^4(x)

Solution

\frac{d}{d x} (\frac{1}{4} sin^{4} (x))

Solution

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

Solution steps

\frac{d}{d x} (\frac{1}{4} sin^{4} (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{4} \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)

= \frac{1}{4} \cdot 4 (sin (x))^{3} cos (x)

Simplify

\frac{1}{4} \cdot 4 sin^{3} (x) cos (x) : sin^{3} (x) cos (x)

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

Popular Examples

limit as x approaches infinity of 1+2^x

x \to \infty lim (1 + 2^{x})

tangent of y=x^2-1,(5,24)tangent of

y = x^{2} - 1, (5, 24)

derivative of x^5*ln(x)

\frac{d}{d x} (x^{5} \cdot ln (x))

derivative of sqrt(x^2-a^2)

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

sum from n=0 to infinity of 1/(3^{n-1)}

n = 0 \sum \infty \frac{1}{3 ^{n - 1}}

Frequently Asked Questions (FAQ)

What is the derivative of 1/4 sin^4(x) ?
The derivative of 1/4 sin^4(x) is sin^3(x)cos(x)
What is the first derivative of 1/4 sin^4(x) ?
The first derivative of 1/4 sin^4(x) is sin^3(x)cos(x)