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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (3 x^{2} + 2 y^{2}) = 6 x

= \frac{1}{2 3 x ^{2} + 2 y ^{2}} \cdot 6 x

Simplify

\frac{1}{2 3 x ^{2} + 2 y ^{2}} \cdot 6 x : \frac{3 x}{3 x ^{2} + 2 y ^{2}}

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

y = x^{2} - 3 x, y = 4 x

(x^{2} + 1) \frac{d y}{d x} + 7 x (y - 1) = 0, y (0) = 9

\int x^{2} e^{21 x} d x

2 y^{^{'}} + t y = 2

\int_{4}^{9} \frac{1}{x} d x

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