What is the derivative of (x^4/(x-1)) ?

The derivative of (x^4/(x-1)) is (3x^4-4x^3)/((x-1)^2)

What is the first derivative of (x^4/(x-1)) ?

The first derivative of (x^4/(x-1)) is (3x^4-4x^3)/((x-1)^2)

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\frac{d}{d x} (\frac{x ^{4}}{x - 1})

\frac{3 x ^{4} - 4 x ^{3}}{( x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{4}}{x - 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{4} ) ( x - 1 ) - \frac{d}{d x} ( x - 1 ) x ^{4}}{( x - 1 ) ^{2}}

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

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

= \frac{4 x ^{3} ( x - 1 ) - 1 \cdot x ^{4}}{( x - 1 ) ^{2}}

Simplify

\frac{4 x ^{3} ( x - 1 ) - 1 \cdot x ^{4}}{( x - 1 ) ^{2}} : \frac{3 x ^{4} - 4 x ^{3}}{( x - 1 ) ^{2}}

= \frac{3 x ^{4} - 4 x ^{3}}{( x - 1 ) ^{2}}

x = \frac{12 - y ^{2}}{4}, x = y

y^{^{'}} x + 4 y x = 8, y (0) = 1

\int \frac{1}{( 1 + sin ^{2} ( x ) )} d x

x^{2} - x - 2

\frac{d}{d x} ((10 x + 2)^{x})

What is the derivative of (x^4/(x-1)) ?
The derivative of (x^4/(x-1)) is (3x^4-4x^3)/((x-1)^2)
What is the first derivative of (x^4/(x-1)) ?
The first derivative of (x^4/(x-1)) is (3x^4-4x^3)/((x-1)^2)