What is (\partial)/(\partial x)(x(x^2+y^2)^{1/2}) ?

The answer to (\partial)/(\partial x)(x(x^2+y^2)^{1/2}) is (2x^2+y^2)/((x^2+y^2)^{1/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

f = x, g = (x^{2} + y^{2})^{\frac{1}{2}}

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

\frac{\partial}{\partial x} (x) = 1

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

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

Simplify

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

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

y = 9 e^{9 e^{x} + x}

1 + e^{x}

y^{^{''}} + 2 y^{^{'}} + y = 8 e^{- t}

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

k = 1 \sum \infty \frac{2 ^{k}}{k !}

What is (\partial)/(\partial x)(x(x^2+y^2)^{1/2}) ?
The answer to (\partial)/(\partial x)(x(x^2+y^2)^{1/2}) is (2x^2+y^2)/((x^2+y^2)^{1/2)}