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Popular >

derivative of 1/(ax+b)

Solution

\frac{d}{d x} (\frac{1}{a x + b})

Solution

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

Solution steps

\frac{d}{d x} (\frac{1}{a x + b})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((a x + b)^{- 1})

Apply the chain rule:

- \frac{1}{( a x + b ) ^{2}} \frac{d}{d x} (a x + b)

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

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

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

Simplify

- \frac{1}{( a x + b ) ^{2}} a : - \frac{a}{( a x + b ) ^{2}}

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

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integral of (5t-2)/(t+1)

\int \frac{5 t - 2}{t + 1} d t

derivative of x/(12+1)

\frac{d}{d x} (\frac{x}{12} + 1)

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\int_{1}^{2} 2 x^{3} - 4 d x

(\partial}{\partial x}(\frac{5y^2)/x)

\frac{\partial}{\partial x} (\frac{5 y ^{2}}{x})

Frequently Asked Questions (FAQ)

What is the derivative of 1/(ax+b) ?
The derivative of 1/(ax+b) is -a/((ax+b)^2)
What is the first derivative of 1/(ax+b) ?
The first derivative of 1/(ax+b) is -a/((ax+b)^2)