What is (\partial)/(\partial y)(sqrt(5x^2+2y^2)) ?

The answer to (\partial)/(\partial y)(sqrt(5x^2+2y^2)) is (2y)/(sqrt(5x^2+2y^2))

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(\partial)/(\partial y)(sqrt(5x^2+2y^2))

\frac{\partial}{\partial y} (5 x^{2} + 2 y^{2})

\frac{2 y}{5 x ^{2} + 2 y ^{2}}

Solution steps

\frac{\partial}{\partial y} (5 x^{2} + 2 y^{2})

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 5 x ^{2} + 2 y ^{2}} \frac{\partial}{\partial y} (5 x^{2} + 2 y^{2})

= \frac{1}{2 5 x ^{2} + 2 y ^{2}} \frac{\partial}{\partial y} (5 x^{2} + 2 y^{2})

\frac{\partial}{\partial y} (5 x^{2} + 2 y^{2}) = 4 y

= \frac{1}{2 5 x ^{2} + 2 y ^{2}} \cdot 4 y

Simplify

\frac{1}{2 5 x ^{2} + 2 y ^{2}} \cdot 4 y : \frac{2 y}{5 x ^{2} + 2 y ^{2}}

= \frac{2 y}{5 x ^{2} + 2 y ^{2}}

\int 13 cos^{3} (x) d x

\frac{d P}{d t} = \frac{P}{5} - \frac{P ^{2}}{75}, P (0) = 5

y = - sin (x)

\int \frac{x}{1 + x ^{2}} d x

\frac{( e ^{- 4 s} )}{s ^{2}}

What is (\partial)/(\partial y)(sqrt(5x^2+2y^2)) ?
The answer to (\partial)/(\partial y)(sqrt(5x^2+2y^2)) is (2y)/(sqrt(5x^2+2y^2))