What is the derivative of (x^2/(x^4)) ?

The derivative of (x^2/(x^4)) is -2/(x^3)

What is the first derivative of (x^2/(x^4)) ?

The first derivative of (x^2/(x^4)) is -2/(x^3)

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\frac{d}{d x} (\frac{x ^{2}}{x ^{4}})

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

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{x ^{4}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) x ^{4} - \frac{d}{d x} ( x ^{4} ) x ^{2}}{( x ^{4} ) ^{2}}

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{1}{1 - x})

\int coth^{2} (x) d x

\int \frac{1}{9 - x ^{2}} d x

\int e^{- k N x} d x

2 (x - 6)^{3}

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