What is the derivative of (x^4/((1+2x)^3)) ?

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((1 + 2 x)^{3}) = 6 (1 + 2 x)^{2}

= \frac{4 x ^{3} ( 1 + 2 x ) ^{3} - 6 ( 1 + 2 x ) ^{2} x ^{4}}{( ( 1 + 2 x ) ^{3} ) ^{2}}

Simplify

\frac{4 x ^{3} ( 1 + 2 x ) ^{3} - 6 ( 1 + 2 x ) ^{2} x ^{4}}{( ( 1 + 2 x ) ^{3} ) ^{2}} : \frac{2 x ^{3} ( x + 2 )}{( 1 + 2 x ) ^{4}}

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

\frac{x ^{6} - 1}{x - 1}

\int \frac{1}{2 x ^{2} + 4 x + 5} d x

\frac{d}{d x} (\frac{x ^{2} + 6}{sin ^{4} ( x )})

f (x) = - 9 e^{x^{- 9}}

\frac{d}{d x} (- \frac{2}{1 - 2 x})

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