What is (\partial)/(\partial y)(x/(x^4-y^7)) ?

The answer to (\partial)/(\partial y)(x/(x^4-y^7)) is (7xy^6)/((x^4-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 y)(x/(x^4-y^7))

\frac{\partial}{\partial y} (\frac{x}{x ^{4} - y ^{7}})

\frac{7 x y ^{6}}{( x ^{4} - y ^{7} ) ^{2}}

Solution steps

\frac{\partial}{\partial y} (\frac{x}{x ^{4} - y ^{7}})

Treat

x

as a constant

Take the constant out:

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

= x \frac{\partial}{\partial y} (\frac{1}{x ^{4} - y ^{7}})

Apply exponent rule:

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

= x \frac{\partial}{\partial y} ((x^{4} - y^{7})^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{4} - y ^{7} ) ^{2}} \frac{\partial}{\partial y} (x^{4} - y^{7})

= - \frac{1}{( x ^{4} - y ^{7} ) ^{2}} \frac{\partial}{\partial y} (x^{4} - y^{7})

\frac{\partial}{\partial y} (x^{4} - y^{7}) = - 7 y^{6}

= x (- \frac{1}{( x ^{4} - y ^{7} ) ^{2}} (- 7 y^{6}))

Simplify

x (- \frac{1}{( x ^{4} - y ^{7} ) ^{2}} (- 7 y^{6})) : \frac{7 x y ^{6}}{( x ^{4} - y ^{7} ) ^{2}}

= \frac{7 x y ^{6}}{( x ^{4} - y ^{7} ) ^{2}}

f (x) = \frac{x ^{3}}{8}

\int \frac{ln ( 5 x )}{x} d x

\int \frac{y ^{2}}{25 + y ^{2}} d y

\frac{d}{d n} ((1 + i)^{n})

f (x) = - \frac{3}{x ^{4}}

What is (\partial)/(\partial y)(x/(x^4-y^7)) ?
The answer to (\partial)/(\partial y)(x/(x^4-y^7)) is (7xy^6)/((x^4-y^7)^2)