What is (\partial)/(\partial u)(ln(5u^2+uv)) ?

The answer to (\partial)/(\partial u)(ln(5u^2+uv)) is (10u+v)/(5u^2+uv)

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(\partial)/(\partial u)(ln(5u^2+uv))

\frac{\partial}{\partial u} (ln (5 u^{2} + uv))

\frac{10 u + v}{5 u ^{2} + uv}

Solution steps

\frac{\partial}{\partial u} (ln (5 u^{2} + uv))

Treat

v

as a constant

Apply the chain rule:

\frac{1}{5 u ^{2} + uv} \frac{\partial}{\partial u} (5 u^{2} + uv)

= \frac{1}{5 u ^{2} + uv} \frac{\partial}{\partial u} (5 u^{2} + uv)

\frac{\partial}{\partial u} (5 u^{2} + uv) = 10 u + v

= \frac{1}{5 u ^{2} + uv} (10 u + v)

Simplify

\frac{1}{5 u ^{2} + uv} (10 u + v) : \frac{10 u + v}{5 u ^{2} + uv}

= \frac{10 u + v}{5 u ^{2} + uv}

\int (8 x - 3) d x

x \to 0 lim (\frac{x ^{3}}{x ^{2} + 1})

(2.5) (7.3)

x \to 0 lim (e^{π})

\frac{d}{d x} (ln (2 x + 2))

What is (\partial)/(\partial u)(ln(5u^2+uv)) ?
The answer to (\partial)/(\partial u)(ln(5u^2+uv)) is (10u+v)/(5u^2+uv)