What is (\partial)/(\partial x)(sqrt(5x^2+4y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(5x^2+4y^2)) is (5x)/(sqrt(5x^2+4y^2))

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(\partial)/(\partial x)(sqrt(5x^2+4y^2))

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

\frac{5 x}{5 x ^{2} + 4 y ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 5 x ^{2} + 4 y ^{2}} \frac{\partial}{\partial x} (5 x^{2} + 4 y^{2})

= \frac{1}{2 5 x ^{2} + 4 y ^{2}} \frac{\partial}{\partial x} (5 x^{2} + 4 y^{2})

\frac{\partial}{\partial x} (5 x^{2} + 4 y^{2}) = 10 x

= \frac{1}{2 5 x ^{2} + 4 y ^{2}} \cdot 10 x

Simplify

\frac{1}{2 5 x ^{2} + 4 y ^{2}} \cdot 10 x : \frac{5 x}{5 x ^{2} + 4 y ^{2}}

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

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What is (\partial)/(\partial x)(sqrt(5x^2+4y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(5x^2+4y^2)) is (5x)/(sqrt(5x^2+4y^2))