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Popular >

derivative of ((3x^3+6))/x

Solution

derivative of

\frac{( 3 x ^{3} + 6 )}{x}

Solution

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

Solution steps

\frac{d}{d x} (\frac{3 x ^{3} + 6}{x})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (3 x^{3} + 6) = 9 x^{2}

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

= \frac{9 x ^{2} x - 1 \cdot ( 3 x ^{3} + 6 )}{x ^{2}}

Simplify

\frac{9 x ^{2} x - 1 \cdot ( 3 x ^{3} + 6 )}{x ^{2}} : \frac{6 x ^{3} - 6}{x ^{2}}

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

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Frequently Asked Questions (FAQ)

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