What is (\partial)/(\partial x)(ln(2x+2ct)) ?

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

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(\partial)/(\partial x)(ln(2x+2ct))

\frac{\partial}{\partial x} (ln (2 x + 2 c t))

\frac{1}{x + c t}

Solution steps

\frac{\partial}{\partial x} (ln (2 x + 2 c t))

Treat

c, t

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{2 x + 2 c t} \cdot 2

Simplify

\frac{1}{2 x + 2 c t} \cdot 2 : \frac{1}{x + c t}

= \frac{1}{x + c t}

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