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

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

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

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

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derivative of

y = \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}}

\frac{d}{d x} (\frac{5}{x + 1})

y^{^{'}} x y = x^{2} + 2 y^{2}

\frac{d}{d x} ((\frac{1 - 2 x}{1 + 3 x})^{4})

\int_{- 9}^{9} 1 + x^{2} d x

\frac{2}{1 + x ^{2}}

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