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Popular >

derivative of (x^3/({f)(x)})

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

Popular Examples

integral of 9/(t^2)

\int \frac{9}{t ^{2}} d t

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\int sec (θ) (sec (θ) + tan (θ)) d θ

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x \to 0 lim (\frac{x}{sin ( 12 x )})

integral of (60)/(2x+5)-4

\int \frac{60}{2 x + 5} - 4 d x

integral from 1 to 8 of x^{-2/3}

\int_{1}^{8} x^{- \frac{2}{3}} d x

Frequently Asked Questions (FAQ)

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