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Popular >

derivative of x/(ax^2+b)

Solution

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

Solution

\frac{- a x ^{2} + b}{( a x ^{2} + b ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( a x ^{2} + b ) - \frac{d}{d x} ( a x ^{2} + b ) x}{( a x ^{2} + b ) ^{2}}

\frac{d x}{d x} = 1

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

= \frac{1 \cdot ( a x ^{2} + b ) - 2 a xx}{( a x ^{2} + b ) ^{2}}

1 \cdot (a x^{2} + b) - 2 a xx = - a x^{2} + b

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

Popular Examples

limit as x approaches-4-of x^2+5/(x+4)

x \to - 4 - lim (x^{2} + \frac{5}{x + 4})

integral of 1/(1-0.5x)

\int \frac{1}{1 - 0.5 x} d x

limit as x approaches 10-of 8-x

x \to 10 - lim (8 - x)

(\partial)/(\partial z)(xe^z+xy+z^3-4)

\frac{\partial}{\partial z} (x e^{z} + x y + z^{3} - 4)

integral of e^xsqrt(1-e^{2x)}

\int e^{x} 1 - e^{2 x} d x

Frequently Asked Questions (FAQ)

What is the derivative of x/(ax^2+b) ?
The derivative of x/(ax^2+b) is (-ax^2+b)/((ax^2+b)^2)
What is the first derivative of x/(ax^2+b) ?
The first derivative of x/(ax^2+b) is (-ax^2+b)/((ax^2+b)^2)