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Popular >

derivative of 3x^{-2}-1/x

Solution

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

Solution

- \frac{6}{x ^{3}} + \frac{1}{x ^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (3 x^{- 2}) = - \frac{6}{x ^{3}}

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

= - \frac{6}{x ^{3}} - (- \frac{1}{x ^{2}})

Simplify

= - \frac{6}{x ^{3}} + \frac{1}{x ^{2}}

Popular Examples

(3x^2y^2)dx+(2x^3y+4y^3)dy=0

(3 x^{2} y^{2}) d x + (2 x^{3} y + 4 y^{3}) d y = 0

limit as x approaches-pi/3 of-2cos(x)

x \to - \frac{π}{3} lim (- 2 cos (x))

derivative of sin(x^2+cos^2(x))

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

(\partial)/(\partial x)(2/(2x-y))

\frac{\partial}{\partial x} (\frac{2}{2 x - y})

integral from 1 to infinity of 1/(x^2+5)

\int_{1}^{\infty} \frac{1}{x ^{2} + 5} d x

Frequently Asked Questions (FAQ)

What is the derivative of 3x^{-2}-1/x ?
The derivative of 3x^{-2}-1/x is -6/(x^3)+1/(x^2)
What is the first derivative of 3x^{-2}-1/x ?
The first derivative of 3x^{-2}-1/x is -6/(x^3)+1/(x^2)