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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

Popular Examples

derivative of f(x)= x/(1-ln(x-2))derivative of

f (x) = \frac{x}{1 - ln ( x - 2 )}

limit as t approaches 1 of (t^3+3)^4

t \to 1 lim ((t^{3} + 3)^{4})

(\partial)/(\partial x)(e^{x^7})

\frac{\partial}{\partial x} (e^{x^{7}})

(\partial)/(\partial x)(e^{x^3})

\frac{\partial}{\partial x} (e^{x^{3}})

y^'-1/2 y=(5x-5)y^{-1},y(0)=4

y^{^{'}} - \frac{1}{2} y = (5 x - 5) y^{- 1}, y (0) = 4

Frequently Asked Questions (FAQ)

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