What is (\partial)/(\partial x)(sqrt(4x^2+3y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(4x^2+3y^2)) is (4x)/(sqrt(4x^2+3y^2))

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(\partial)/(\partial x)(sqrt(4x^2+3y^2))

\frac{\partial}{\partial x} (4 x^{2} + 3 y^{2})

\frac{4 x}{4 x ^{2} + 3 y ^{2}}

Solution steps

\frac{\partial}{\partial x} (4 x^{2} + 3 y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 4 x ^{2} + 3 y ^{2}} \frac{\partial}{\partial x} (4 x^{2} + 3 y^{2})

= \frac{1}{2 4 x ^{2} + 3 y ^{2}} \frac{\partial}{\partial x} (4 x^{2} + 3 y^{2})

\frac{\partial}{\partial x} (4 x^{2} + 3 y^{2}) = 8 x

= \frac{1}{2 4 x ^{2} + 3 y ^{2}} \cdot 8 x

Simplify

\frac{1}{2 4 x ^{2} + 3 y ^{2}} \cdot 8 x : \frac{4 x}{4 x ^{2} + 3 y ^{2}}

= \frac{4 x}{4 x ^{2} + 3 y ^{2}}

y^{2} \cdot (\frac{d y}{d x}) + y^{3} = 1

\int \frac{x ^{3} + 1}{x ^{2} + 5 x + 6} d x

\frac{d}{d x} (\frac{1}{2 x ^{2} + 4})

\frac{d}{d x} (750 + 12 x - 0.08 x^{7})

What is (\partial)/(\partial x)(sqrt(4x^2+3y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(4x^2+3y^2)) is (4x)/(sqrt(4x^2+3y^2))