What is (\partial)/(\partial x)(x^8+2^y+x^y) ?

The answer to (\partial)/(\partial x)(x^8+2^y+x^y) is 8x^7+yx^{y-1}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(x^8+2^y+x^y)

\frac{\partial}{\partial x} (x^{8} + 2^{y} + x^{y})

8 x^{7} + y x^{y - 1}

Solution steps

\frac{\partial}{\partial x} (x^{8} + 2^{y} + x^{y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{8}) + \frac{\partial}{\partial x} (2^{y}) + \frac{\partial}{\partial x} (x^{y})

\frac{\partial}{\partial x} (x^{8}) = 8 x^{7}

\frac{\partial}{\partial x} (2^{y}) = 0

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

= 8 x^{7} + 0 + y x^{y - 1}

Simplify

= 8 x^{7} + y x^{y - 1}

What is (\partial)/(\partial x)(x^8+2^y+x^y) ?
The answer to (\partial)/(\partial x)(x^8+2^y+x^y) is 8x^7+yx^{y-1}