What is the derivative of 1/(x^2cos(x)) ?

The derivative of 1/(x^2cos(x)) is -(2cos(x)-xsin(x))/(x^3cos^2(x))

What is the first derivative of 1/(x^2cos(x)) ?

The first derivative of 1/(x^2cos(x)) is -(2cos(x)-xsin(x))/(x^3cos^2(x))

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\frac{d}{d x} (\frac{1}{x ^{2} cos ( x )})

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

Solution steps

\frac{d}{d x} (\frac{1}{x ^{2} cos ( x )})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((x^{2} cos (x))^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{2} cos ( x ) ) ^{2}} \frac{d}{d x} (x^{2} cos (x))

= - \frac{1}{( x ^{2} cos ( x ) ) ^{2}} \frac{d}{d x} (x^{2} cos (x))

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

= - \frac{1}{( x ^{2} cos ( x ) ) ^{2}} (2 x cos (x) - x^{2} sin (x))

Simplify

- \frac{1}{( x ^{2} cos ( x ) ) ^{2}} (2 x cos (x) - x^{2} sin (x)) : - \frac{2 cos ( x ) - x sin ( x )}{x ^{3} cos ^{2} ( x )}

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

y^{^{'}} = 135 y x^{4}

f (x) = (5 x^{3} + 2) (3 x^{3} + 2)

n = 1 \sum \infty \frac{n - 1}{9 n - 1}

e^{- t} (t^{2} + 4 t + 5)

y^{^{'}} + 4 e^{x + y} = 0

What is the derivative of 1/(x^2cos(x)) ?
The derivative of 1/(x^2cos(x)) is -(2cos(x)-xsin(x))/(x^3cos^2(x))
What is the first derivative of 1/(x^2cos(x)) ?
The first derivative of 1/(x^2cos(x)) is -(2cos(x)-xsin(x))/(x^3cos^2(x))