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Popular >

derivative of sin^4(sqrt(x))

Solution

derivative of

sin^{4} (x)

Solution

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

Solution steps

\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)) = \frac{cos ( x )}{2 x}

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

Simplify

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

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

Popular Examples

inverse oflaplace 1/(s^2(s+sqrt(2)))inverse laplace

\frac{1}{s ^{2} ( s + 2 )}

integral from 0 to 7 of 9800pi(7-y)

\int_{0}^{7} 9800 π (7 - y) d y

tangent of y= 1/((1+x^2),(-1, 1/2))tangent of

y = \frac{1}{( 1 + x ^{2} ) , ( - 1 , \frac{1}{2} )}

integral of (xe^{2x})

\int (x e^{2 x}) d x

(d^2y)/(dx^2)+6(dy)/(dx)+5y=0

\frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 5 y = 0

Frequently Asked Questions (FAQ)

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