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Popular >

derivative of (8x^2+2)/(x^2)

Solution

derivative of

\frac{8 x ^{2} + 2}{x ^{2}}

Solution

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

Solution steps

\frac{d}{d x} (\frac{8 x ^{2} + 2}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 8 x ^{2} + 2 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 8 x ^{2} + 2 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (8 x^{2} + 2) = 16 x

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

= \frac{16 x x ^{2} - 2 x ( 8 x ^{2} + 2 )}{( x ^{2} ) ^{2}}

Simplify

\frac{16 x x ^{2} - 2 x ( 8 x ^{2} + 2 )}{( x ^{2} ) ^{2}} : - \frac{4}{x ^{3}}

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

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x \to 1 lim (sin (\frac{1}{x - 1}))

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\int (x + x^{\frac{3}{4}}) d x

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Frequently Asked Questions (FAQ)

What is the derivative of (8x^2+2)/(x^2) ?
The derivative of (8x^2+2)/(x^2) is -4/(x^3)
What is the first derivative of (8x^2+2)/(x^2) ?
The first derivative of (8x^2+2)/(x^2) is -4/(x^3)