What is (\partial)/(\partial x)(1/(x-a)) ?

The answer to (\partial)/(\partial x)(1/(x-a)) is -1/((x-a)^2)

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(\partial)/(\partial x)(1/(x-a))

\frac{\partial}{\partial x} (\frac{1}{x - a})

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

Solution steps

\frac{\partial}{\partial x} (\frac{1}{x - a})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x - a) = 1

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

Simplify

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

\int sin (x) sec^{2} (x) d x

\frac{\partial}{\partial x} (4 x^{3} + 4 x y^{2})

e^{- 3 t}

(t^{2} + 16) (\frac{d x}{d t}) = (x^{2} + 25), x (0) = 5

x \to 0 lim ((1 - 5 x)^{\frac{1}{x}})

What is (\partial)/(\partial x)(1/(x-a)) ?
The answer to (\partial)/(\partial x)(1/(x-a)) is -1/((x-a)^2)