What is (\partial)/(\partial x)(1/(x+ct)) ?

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

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(\partial)/(\partial x)(1/(x+ct))

\frac{\partial}{\partial x} (\frac{1}{x + c t})

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

Solution steps

\frac{\partial}{\partial x} (\frac{1}{x + c t})

Treat

c, t

as a constant

Apply exponent rule:

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

= \frac{\partial}{\partial x} ((x + c t)^{- 1})

Apply the chain rule:

- \frac{1}{( x + c t ) ^{2}} \frac{\partial}{\partial x} (x + c t)

= - \frac{1}{( x + c t ) ^{2}} \frac{\partial}{\partial x} (x + c t)

\frac{\partial}{\partial x} (x + c t) = 1

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

Simplify

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

\int_{l n (2)}^{3} (5 e^{x}) d x

x \to 2 lim (x - 3)

\int_{0}^{1} (x^{2} - x^{3}) d x

x \to 0 lim (\frac{1 - cos ( 7 x )}{4 x ^{2}})

\frac{d}{d x} (A (2 x e^{x} + e^{x} x^{2}))

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