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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

= \frac{sin ( 2 x ) x - 1 \cdot sin ^{2} ( x )}{x ^{2}}

Simplify

= \frac{x sin ( 2 x ) - sin ^{2} ( x )}{x ^{2}}

Popular Examples

derivative of 1/3 x^3+8x^2+63x+7 derivative of

\frac{1}{3} x^{3} + 8 x^{2} + 63 x + 7

integral from-4pi to 4pi of sin^2(x)+1

\int_{- 4 π}^{4 π} sin^{2} (x) + 1 d x

limit as x approaches 2-of 4

x \to 2 - lim (4)

y^{''}x+(2/x-(2x)/(1+x^2))*y^'=0

y^{^{''}} x + (\frac{2}{x} - \frac{2 x}{1 + x ^{2}}) \cdot y^{^{'}} = 0

derivative of 2cos(x-4sin(x))

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

Frequently Asked Questions (FAQ)

What is the derivative of (sin^2(x)/x) ?
The derivative of (sin^2(x)/x) is (xsin(2x)-sin^2(x))/(x^2)
What is the first derivative of (sin^2(x)/x) ?
The first derivative of (sin^2(x)/x) is (xsin(2x)-sin^2(x))/(x^2)