What is (\partial)/(\partial x)(3(y/x)^{1/2}) ?

The answer to (\partial)/(\partial x)(3(y/x)^{1/2}) is -(3y^{1/2})/(2x^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(3(y/x)^{1/2})

\frac{\partial}{\partial x} (3 (\frac{y}{x})^{\frac{1}{2}})

- \frac{3 y ^{\frac{1}{2}}}{2 x ^{\frac{3}{2}}}

Solution steps

\frac{\partial}{\partial x} (3 (\frac{y}{x})^{\frac{1}{2}})

Treat

y

as a constant

Take the constant out:

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

= 3 \frac{\partial}{\partial x} ((\frac{y}{x})^{\frac{1}{2}})

Apply the chain rule:

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

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

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

= 3 \cdot \frac{1}{2 ( \frac{y}{x} ) ^{\frac{1}{2}}} (- \frac{y}{x ^{2}})

Simplify

3 \cdot \frac{1}{2 ( \frac{y}{x} ) ^{\frac{1}{2}}} (- \frac{y}{x ^{2}}) : - \frac{3 y ^{\frac{1}{2}}}{2 x ^{\frac{3}{2}}}

= - \frac{3 y ^{\frac{1}{2}}}{2 x ^{\frac{3}{2}}}

f^{^{''}} (x) = 4 x

\int_{0}^{3} π (6 3 y)^{2} d y

(x^{2} + y^{2}) d x - x y d y = 0

\int \frac{6}{x} d x

\int \frac{1}{( 1 + x ) ^{4}} d x

What is (\partial)/(\partial x)(3(y/x)^{1/2}) ?
The answer to (\partial)/(\partial x)(3(y/x)^{1/2}) is -(3y^{1/2})/(2x^{3/2)}