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

The answer to (\partial)/(\partial x)((x^4+x-y)^7) is 7(x^4+x-y)^6(4x^3+1)

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(\partial)/(\partial x)((x^4+x-y)^7)

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

7 (x^{4} + x - y)^{6} (4 x^{3} + 1)

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x^{4} + x - y) = 4 x^{3} + 1

= 7 (x^{4} + x - y)^{6} (4 x^{3} + 1)

\int ln (3 x + 2) d x

sin^{7} (x)

\int - 2 + 12 x - 12 x^{2} d x

\int \frac{e ^{8 x}}{e ^{8 x} + 4} d x

f (x) = x^{2} + 3 x - 1, at x = 0

What is (\partial)/(\partial x)((x^4+x-y)^7) ?
The answer to (\partial)/(\partial x)((x^4+x-y)^7) is 7(x^4+x-y)^6(4x^3+1)