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Popular >

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

Solution

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

Solution

- \frac{3}{x ^{4}} + \frac{1}{x ^{2}} + 2 x

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (\frac{1}{x ^{3}}) = - \frac{3}{x ^{4}}

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

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

= - \frac{3}{x ^{4}} - (- \frac{1}{x ^{2}}) + 2 x

Simplify

= - \frac{3}{x ^{4}} + \frac{1}{x ^{2}} + 2 x

Popular Examples

derivative of 1/(sqrt(x^2+y^2))

\frac{d}{d x} (\frac{1}{x ^{2} + y ^{2}})

(\partial)/(\partial x)(ln(9x^2+y^2+5))

\frac{\partial}{\partial x} (ln (9 x^{2} + y^{2} + 5))

(\partial)/(\partial t)(1-t)

\frac{\partial}{\partial t} (1 - t)

limit as x approaches 7 of x/(sqrt(x-3))

x \to 7 lim (\frac{x}{x - 3})

limit as x approaches 3 of (sin(5x))/x

x \to 3 lim (\frac{sin ( 5 x )}{x})

Frequently Asked Questions (FAQ)

What is the derivative of 1/(x^3-1/x+x^2) ?
The derivative of 1/(x^3-1/x+x^2) is -3/(x^4)+1/(x^2)+2x
What is the first derivative of 1/(x^3-1/x+x^2) ?
The first derivative of 1/(x^3-1/x+x^2) is -3/(x^4)+1/(x^2)+2x