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Popular Calculus >

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

Solution

\frac{d}{d x} (\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}}

Graph

Popular Examples

integral from-1 to 3 of sqrt(1+(6y+2)^2)

\int_{- 1}^{3} 1 + (6 y + 2)^{2} d y

integral of (a+bx^3)^2

\int (a + b x^{3})^{2} d x

derivative of-cos(\sqrt[3]{x}-3+pi/2)

\frac{d}{d x} (- cos (3 x - 3 + \frac{π}{2}))

limit as x approaches 1-of sqrt(1-x)

x \to 1 - lim (1 - x)

limit as x approaches 4 of (x-4)/(2-sqrt(8-x))

x \to 4 lim (\frac{x - 4}{2 - 8 - 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)