What is (\partial)/(\partial x)(ln(x^2u)) ?

The answer to (\partial)/(\partial x)(ln(x^2u)) is 2/x

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(\partial)/(\partial x)(ln(x^2u))

\frac{\partial}{\partial x} (ln (x^{2} u))

\frac{2}{x}

Solution steps

\frac{\partial}{\partial x} (ln (x^{2} u))

Treat

u

as a constant

Apply the chain rule:

\frac{1}{x ^{2} u} \frac{\partial}{\partial x} (x^{2} u)

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

\frac{\partial}{\partial x} (x^{2} u) = 2 ux

= \frac{1}{x ^{2} u} \cdot 2 ux

Simplify

\frac{1}{x ^{2} u} \cdot 2 ux : \frac{2}{x}

= \frac{2}{x}

f (x) = (2 x + 3)^{6} (x - 2)^{4}

\int x + π d x

f (x) = 7 x + 8

e^{- 0}

\frac{d}{d x} (x \cdot sin (y))

What is (\partial)/(\partial x)(ln(x^2u)) ?
The answer to (\partial)/(\partial x)(ln(x^2u)) is 2/x