What is the derivative of 1/(x+a) ?

The derivative of 1/(x+a) is -1/((x+a)^2)

What is the first derivative of 1/(x+a) ?

The first derivative of 1/(x+a) is -1/((x+a)^2)

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{1}{x - 1}

\int ln (e^{2 x - 1}) d x

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

x sin (x^{3})

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