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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

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

\frac{d}{d x} (3 + 2 x) = 2

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

Expand

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

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

Popular Examples

(\partial)/(\partial x)((x-3)^2)

\frac{\partial}{\partial x} ((x - 3)^{2})

derivative of (x^3-x^4)

\frac{d}{d x} ((x^{3} - x)^{4})

integral from 0 to infinity of 2/(1+x^2)

\int_{0}^{\infty} \frac{2}{1 + x ^{2}} d x

derivative of x^2tan(x)derivative of

x^{2} tan (x)

(\partial)/(\partial x)(ln(1/x))

\frac{\partial}{\partial x} (ln (\frac{1}{x}))

Frequently Asked Questions (FAQ)

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