What is the derivative of xsqrt(x^2+y^2) ?

The derivative of xsqrt(x^2+y^2) is (2x^2+xy\frac{dy)/(dx)+y^2}{sqrt(x^2+y^2)}

What is the first derivative of xsqrt(x^2+y^2) ?

The first derivative of xsqrt(x^2+y^2) is (2x^2+xy\frac{dy)/(dx)+y^2}{sqrt(x^2+y^2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{2} + y^{2}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

What is the derivative of xsqrt(x^2+y^2) ?
The derivative of xsqrt(x^2+y^2) is (2x^2+xy\frac{dy)/(dx)+y^2}{sqrt(x^2+y^2)}
What is the first derivative of xsqrt(x^2+y^2) ?
The first derivative of xsqrt(x^2+y^2) is (2x^2+xy\frac{dy)/(dx)+y^2}{sqrt(x^2+y^2)}