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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(ysqrt(x^2+y^2))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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