What is the derivative of x/(x^3) ?

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

What is the first derivative of x/(x^3) ?

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

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derivative of

\frac{x}{x ^{3}}

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

x^{2} - 2 x - 1, - 1, 2

\int x^{2} + y^{2} + z^{2} d x

\int \frac{6 x ^{3} - 8 x}{x ^{4} - 16} d x

\int_{0}^{6} \frac{5 t}{( t - 7 ) ^{2}} d t

\int \frac{1}{( 4 - x ^{2} ) ^{3}} d x

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