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

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

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

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

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derivative of

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

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

Solution steps

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

\frac{d}{d x} (sin (x)) = cos (x)

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

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

Simplify

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

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

y = (\frac{5}{x} + x) (\frac{5}{x} - x)

y^{^{''}} + y^{^{'}} - 2 = e^{- t}

\int \frac{y ^{2} + 14 y + 49}{( y ^{2} + 49 ) ^{2}} d y

y^{^{'}} + (1 + 3 x^{2}) y = 3 + 9 x^{2}

\int \frac{1 + 2 t ^{3}}{t} d t

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