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Popular >

derivative of (x^2)/(3+8x)

Solution

derivative of

\frac{x ^{2}}{3 + 8 x}

Solution

\frac{6 x + 8 x ^{2}}{( 3 + 8 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{3 + 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} ) ( 3 + 8 x ) - \frac{d}{d x} ( 3 + 8 x ) x ^{2}}{( 3 + 8 x ) ^{2}}

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

\frac{d}{d x} (3 + 8 x) = 8

= \frac{2 x ( 3 + 8 x ) - 8 x ^{2}}{( 3 + 8 x ) ^{2}}

Expand

2 x (3 + 8 x) - 8 x^{2} : 6 x + 8 x^{2}

= \frac{6 x + 8 x ^{2}}{( 3 + 8 x ) ^{2}}

Popular Examples

integral of 3sqrt(t+1)

\int 3 t + 1 d t

derivative of x^3-3x^2+5x-2

\frac{d}{d x} (x^{3} - 3 x^{2} + 5 x - 2)

derivative of ae^x+b/x+c/(x^2)

\frac{d}{d x} (a e^{x} + \frac{b}{x} + \frac{c}{x ^{2}})

tangent of f(x)=7x^2-x^3,\at x=1 tangent of

f (x) = 7 x^{2} - x^{3}, at x = 1

integral from 0 to 1 of ln(4+x^2)

\int_{0}^{1} ln (4 + x^{2}) d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^2)/(3+8x) ?
The derivative of (x^2)/(3+8x) is (6x+8x^2)/((3+8x)^2)
What is the first derivative of (x^2)/(3+8x) ?
The first derivative of (x^2)/(3+8x) is (6x+8x^2)/((3+8x)^2)