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

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

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

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

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derivative of

f (x) = \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 y}{d x} = (y - 1)^{- 3}

\int \frac{sin ( θ )}{cos ^{2} ( θ ) - cos ( θ ) - 2} d θ

y (θ) = cos (θ^{2})

x \to \infty lim (2 x^{4})

\frac{d y}{d x} = 2 y - x y

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