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

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

Popular >

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

x^{2} y^{^{''}} - x y^{^{'}} + y = \frac{1}{x}

\int_{0}^{0.5} 500 x d x

f (x) = 6 x^{2} + 2 x - 7

\int_{0}^{16} x e^{- x} d x

x \to 0 - lim (\frac{11}{tan ( x )})

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