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Popular >

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

Solution

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

Solution

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

Solution steps

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

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

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

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

Expand

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

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

Graph

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Frequently Asked Questions (FAQ)

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