What is the derivative of (sin^2(x))/(x^2) ?

The derivative of (sin^2(x))/(x^2) is (xsin(2x)-2sin^2(x))/(x^3)

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

The first derivative of (sin^2(x))/(x^2) is (xsin(2x)-2sin^2(x))/(x^3)

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derivative of

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

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

Solution steps

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (4 x^{2} - 14 x - 8 a)

csc^{3} (x)

2 x^{2} - x + 1

\frac{d}{d a} (sin^{2} (a) + cos^{4} (a))

e^{2} x - 2

What is the derivative of (sin^2(x))/(x^2) ?
The derivative of (sin^2(x))/(x^2) is (xsin(2x)-2sin^2(x))/(x^3)
What is the first derivative of (sin^2(x))/(x^2) ?
The first derivative of (sin^2(x))/(x^2) is (xsin(2x)-2sin^2(x))/(x^3)