What is (\partial)/(\partial x)((x^5+x-y)^6) ?

The answer to (\partial)/(\partial x)((x^5+x-y)^6) is 6(x^5+x-y)^5(5x^4+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)((x^5+x-y)^6)

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

6 (x^{5} + x - y)^{5} (5 x^{4} + 1)

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x^{5} + x - y) = 5 x^{4} + 1

= 6 (x^{5} + x - y)^{5} (5 x^{4} + 1)

What is (\partial)/(\partial x)((x^5+x-y)^6) ?
The answer to (\partial)/(\partial x)((x^5+x-y)^6) is 6(x^5+x-y)^5(5x^4+1)