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Popular Calculus >

derivative of (2x^3-6)/(x^4)

Solution

derivative of

\frac{2 x ^{3} - 6}{x ^{4}}

Solution

\frac{2 ( - x ^{3} + 12 )}{x ^{5}}

Solution steps

\frac{d}{d x} (\frac{2 x ^{3} - 6}{x ^{4}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x ^{3} - 6 ) x ^{4} - \frac{d}{d x} ( x ^{4} ) ( 2 x ^{3} - 6 )}{( x ^{4} ) ^{2}}

\frac{d}{d x} (2 x^{3} - 6) = 6 x^{2}

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

= \frac{6 x ^{2} x ^{4} - 4 x ^{3} ( 2 x ^{3} - 6 )}{( x ^{4} ) ^{2}}

Simplify

\frac{6 x ^{2} x ^{4} - 4 x ^{3} ( 2 x ^{3} - 6 )}{( x ^{4} ) ^{2}} : \frac{2 ( - x ^{3} + 12 )}{x ^{5}}

= \frac{2 ( - x ^{3} + 12 )}{x ^{5}}

Graph

Popular Examples

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\frac{\partial}{\partial x} (30 x^{5} y^{4} - 20 x^{4} y^{3})

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x \to - 2 lim (\frac{1}{x ^{2}})

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Frequently Asked Questions (FAQ)

What is the derivative of (2x^3-6)/(x^4) ?
The derivative of (2x^3-6)/(x^4) is (2(-x^3+12))/(x^5)
What is the first derivative of (2x^3-6)/(x^4) ?
The first derivative of (2x^3-6)/(x^4) is (2(-x^3+12))/(x^5)