What is the derivative of cos(xx^{-2}) ?

The derivative of cos(xx^{-2}) is -(sin(x))/(x^2)-(2cos(x))/(x^3)

What is the first derivative of cos(xx^{-2}) ?

The first derivative of cos(xx^{-2}) is -(sin(x))/(x^2)-(2cos(x))/(x^3)

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (x), g = x^{- 2}

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (\frac{3 y ^{2}}{x})

\int (3 x^{5} - x^{3} + 6) d x

\int_{0}^{8} \frac{x}{4} d x

x \to - 7 lim (\frac{x + 2}{x})

\int 64 - 4 x^{2} d x

What is the derivative of cos(xx^{-2}) ?
The derivative of cos(xx^{-2}) is -(sin(x))/(x^2)-(2cos(x))/(x^3)
What is the first derivative of cos(xx^{-2}) ?
The first derivative of cos(xx^{-2}) is -(sin(x))/(x^2)-(2cos(x))/(x^3)