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Popular >

derivative of (x^2)/(1+4x)

Solution

derivative of

\frac{x ^{2}}{1 + 4 x}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (1 + 4 x) = 4

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

Expand

2 x (1 + 4 x) - 4 x^{2} : 2 x + 4 x^{2}

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

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\frac{d}{d x} (9 - x^{8})

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\int y^{- \frac{1}{2}} d y

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

Frequently Asked Questions (FAQ)

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