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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\frac{d}{d x} (\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}}

x \to - 6 lim (- 12)

\frac{d}{d θ} (1 - cos (θ))

\int \frac{1}{x ( x - 3 )} d x

f (x) = 10 x^{3}

\int \frac{( ln ( x ) ) ^{34}}{x} d x

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)