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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\frac{d}{d x} ((5 x + 6)^{2})

f (x) = 4 x, at x = 9

5 \frac{d y}{d x} + 2 x = 3

\int \frac{3 x ^{2} + 1}{x ^{3} + x} d x

\frac{d}{d x} f (x) = \frac{2}{5} x^{5} - 4 x^{3} + 9 x^{2} - 6 x - 2

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