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)

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(\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)

y = 9 e^{- x} + e^{2 x}

\int 8 x^{3} - cos (4 x) d x

e

x^{2} \frac{d y}{d x} = x y + y^{2}

f (x) = \frac{3}{x}, (- 8, - \frac{3}{8})

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)