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Popular >

derivative of (x^2/(5+8x))

Solution

\frac{d}{d x} (\frac{x ^{2}}{5 + 8 x})

Solution

\frac{10 x + 8 x ^{2}}{( 5 + 8 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{5 + 8 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 5 + 8 x ) - \frac{d}{d x} ( 5 + 8 x ) x ^{2}}{( 5 + 8 x ) ^{2}}

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

\frac{d}{d x} (5 + 8 x) = 8

= \frac{2 x ( 5 + 8 x ) - 8 x ^{2}}{( 5 + 8 x ) ^{2}}

Expand

2 x (5 + 8 x) - 8 x^{2} : 10 x + 8 x^{2}

= \frac{10 x + 8 x ^{2}}{( 5 + 8 x ) ^{2}}

Popular Examples

integral of 1/((x-5)(x-3))

\int \frac{1}{( x - 5 ) ( x - 3 )} d x

laplacetransform 3e^{-3t}laplace transform

3 e^{- 3 t}

derivative of sin^2(x+1)

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

limit as x approaches 0-of (8x^4-3x)/x

x \to 0 - lim (\frac{8 x ^{4} - 3 x}{x})

limit as x approaches 0 of 2x-2

x \to 0 lim (2 x - 2)

Frequently Asked Questions (FAQ)

What is the derivative of (x^2/(5+8x)) ?
The derivative of (x^2/(5+8x)) is (10x+8x^2)/((5+8x)^2)
What is the first derivative of (x^2/(5+8x)) ?
The first derivative of (x^2/(5+8x)) is (10x+8x^2)/((5+8x)^2)