What is (\partial)/(\partial x)(m/(x^ay^bz^c)) ?

The answer to (\partial)/(\partial x)(m/(x^ay^bz^c)) is -(amx^{-a-1})/(z^cy^b)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(m/(x^ay^bz^c))

\frac{\partial}{\partial x} (\frac{m}{x ^{a} y ^{b} z ^{c}})

- \frac{am x ^{- a - 1}}{z ^{c} y ^{b}}

Solution steps

\frac{\partial}{\partial x} (\frac{m}{x ^{a} y ^{b} z ^{c}})

Treat

a, c, m, y, b, z

as constants

Take the constant out:

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

= \frac{m}{y ^{b} z ^{c}} \frac{\partial}{\partial x} (\frac{1}{x ^{a}})

Apply exponent rule:

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

= \frac{m}{y ^{b} z ^{c}} \frac{\partial}{\partial x} (x^{- a})

Apply the Power Rule:

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

= \frac{m}{y ^{b} z ^{c}} (- a x^{- a - 1})

Simplify

\frac{m}{y ^{b} z ^{c}} (- a x^{- a - 1}) : - \frac{am x ^{- a - 1}}{z ^{c} y ^{b}}

= - \frac{am x ^{- a - 1}}{z ^{c} y ^{b}}

\frac{\partial}{\partial x} (\frac{3}{8} x y)

\int t^{2} e^{- (s - 1) t} d t

\frac{d}{d x} (a cos (b x + c) + d)

6 x^{2} - 2 x, x^{3} - 6 x + 3

\int (2^{0} - 3^{0})^{x} d x

What is (\partial)/(\partial x)(m/(x^ay^bz^c)) ?
The answer to (\partial)/(\partial x)(m/(x^ay^bz^c)) is -(amx^{-a-1})/(z^cy^b)