What is (\partial)/(\partial x)(x/(x^6-y^7)) ?

The answer to (\partial)/(\partial x)(x/(x^6-y^7)) is (-5x^6-y^7)/((x^6-y^7)^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^6-y^7))

\frac{\partial}{\partial x} (\frac{x}{x ^{6} - y ^{7}})

\frac{- 5 x ^{6} - y ^{7}}{( x ^{6} - y ^{7} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{x}{x ^{6} - y ^{7}})

Treat

y

as a constant

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{\partial}{\partial x} ( x ) ( x ^{6} - y ^{7} ) - \frac{\partial}{\partial x} ( x ^{6} - y ^{7} ) x}{( x ^{6} - y ^{7} ) ^{2}}

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

\frac{\partial}{\partial x} (x^{6} - y^{7}) = 6 x^{5}

= \frac{1 \cdot ( x ^{6} - y ^{7} ) - 6 x ^{5} x}{( x ^{6} - y ^{7} ) ^{2}}

1 \cdot (x^{6} - y^{7}) - 6 x^{5} x = - 5 x^{6} - y^{7}

= \frac{- 5 x ^{6} - y ^{7}}{( x ^{6} - y ^{7} ) ^{2}}

n = 4 \sum \infty (x + 1)^{n}

f (x) = x^{- 8}

y^{^{'}} = - 2 y + t, y (0) = - 5

\int \frac{1}{y ^{2} - 3 y + 2} d y

\int (x^{2} + 3 x + 1) d x

What is (\partial)/(\partial x)(x/(x^6-y^7)) ?
The answer to (\partial)/(\partial x)(x/(x^6-y^7)) is (-5x^6-y^7)/((x^6-y^7)^2)