What is (\partial)/(\partial u)(sqrt(5u^2+8v^2)) ?

The answer to (\partial)/(\partial u)(sqrt(5u^2+8v^2)) is (5u)/(sqrt(5u^2+8v^2))

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(\partial)/(\partial u)(sqrt(5u^2+8v^2))

\frac{\partial}{\partial u} (5 u^{2} + 8 v^{2})

\frac{5 u}{5 u ^{2} + 8 v ^{2}}

Solution steps

\frac{\partial}{\partial u} (5 u^{2} + 8 v^{2})

Treat

v

as a constant

Apply the chain rule:

\frac{1}{2 5 u ^{2} + 8 v ^{2}} \frac{\partial}{\partial u} (5 u^{2} + 8 v^{2})

= \frac{1}{2 5 u ^{2} + 8 v ^{2}} \frac{\partial}{\partial u} (5 u^{2} + 8 v^{2})

\frac{\partial}{\partial u} (5 u^{2} + 8 v^{2}) = 10 u

= \frac{1}{2 5 u ^{2} + 8 v ^{2}} \cdot 10 u

Simplify

\frac{1}{2 5 u ^{2} + 8 v ^{2}} \cdot 10 u : \frac{5 u}{5 u ^{2} + 8 v ^{2}}

= \frac{5 u}{5 u ^{2} + 8 v ^{2}}

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

\frac{d}{d x} (π^{5})

y^{^{''''}} - 5 y^{^{''}} + 4 y = 0

n = 1 \sum \infty arctan (11 n)

\frac{d}{d x} (- x (1 + x^{2})^{- \frac{3}{2}})

What is (\partial)/(\partial u)(sqrt(5u^2+8v^2)) ?
The answer to (\partial)/(\partial u)(sqrt(5u^2+8v^2)) is (5u)/(sqrt(5u^2+8v^2))