What is (\partial)/(\partial x)(0.1*sqrt(x)*y) ?

The answer to (\partial)/(\partial x)(0.1*sqrt(x)*y) is (0.05y)/(sqrt(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(0.1sqrt(x)y)

\frac{\partial}{\partial x} (0.1 \cdot x \cdot y)

\frac{0.05 y}{x}

Solution steps

\frac{\partial}{\partial x} (0.1 x y)

Treat

y

as a constant

Take the constant out:

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

= 0.1 y \frac{\partial}{\partial x} (x)

Apply radical rule:

a = a^{\frac{1}{2}}

= 0.1 y \frac{\partial}{\partial x} (x^{\frac{1}{2}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 0.1 y \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

0.1 y \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{0.05 y}{x}

= \frac{0.05 y}{x}

What is (\partial)/(\partial x)(0.1*sqrt(x)*y) ?
The answer to (\partial)/(\partial x)(0.1*sqrt(x)*y) is (0.05y)/(sqrt(x))