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Popular >

derivative of 1/(2x-1/(3x^2))

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

Popular Examples

integral of sin(x)sec^3(x)

\int sin (x) sec^{3} (x) d x

xy^2+3y^2-x^2(dy)/(dx)=0

x y^{2} + 3 y^{2} - x^{2} \frac{d y}{d x} = 0

integral from 2 to sqrt(6 of)x

\int_{2}^{6} x d x

derivative of ((x^2+3)/(x^2-3))^3 derivative of

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

(\partial)/(\partial x)(x*e^{xy})

\frac{\partial}{\partial x} (x \cdot e^{x y})

Frequently Asked Questions (FAQ)

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