What is (\partial)/(\partial x)(x^7y^9-x^6y^8) ?

The answer to (\partial)/(\partial x)(x^7y^9-x^6y^8) is 7y^9x^6-6y^8x^5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(x^7y^9-x^6y^8)

\frac{\partial}{\partial x} (x^{7} y^{9} - x^{6} y^{8})

7 y^{9} x^{6} - 6 y^{8} x^{5}

Solution steps

\frac{\partial}{\partial x} (x^{7} y^{9} - x^{6} y^{8})

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{7} y^{9}) - \frac{\partial}{\partial x} (x^{6} y^{8})

\frac{\partial}{\partial x} (x^{7} y^{9}) = 7 y^{9} x^{6}

\frac{\partial}{\partial x} (x^{6} y^{8}) = 6 y^{8} x^{5}

= 7 y^{9} x^{6} - 6 y^{8} x^{5}

What is (\partial)/(\partial x)(x^7y^9-x^6y^8) ?
The answer to (\partial)/(\partial x)(x^7y^9-x^6y^8) is 7y^9x^6-6y^8x^5