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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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