What is (\partial)/(\partial x)((x^2+x-y)^7) ?

The answer to (\partial)/(\partial x)((x^2+x-y)^7) is 7(x^2+x-y)^6(2x+1)

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(\partial)/(\partial x)((x^2+x-y)^7)

\frac{\partial}{\partial x} ((x^{2} + x - y)^{7})

7 (x^{2} + x - y)^{6} (2 x + 1)

Solution steps

\frac{\partial}{\partial x} ((x^{2} + x - y)^{7})

Treat

y

as a constant

Apply the chain rule:

7 (x^{2} + x - y)^{6} \frac{\partial}{\partial x} (x^{2} + x - y)

= 7 (x^{2} + x - y)^{6} \frac{\partial}{\partial x} (x^{2} + x - y)

\frac{\partial}{\partial x} (x^{2} + x - y) = 2 x + 1

= 7 (x^{2} + x - y)^{6} (2 x + 1)

\frac{d}{d x} (x^{3} + 7 x)

\int_{0}^{1} \frac{1}{1 + x ^{2}} d x

\int e^{1 - 3 x} d x

x \to \infty lim (x^{1})

y^{^{''}} + 2 y = e x + x^{3}

What is (\partial)/(\partial x)((x^2+x-y)^7) ?
The answer to (\partial)/(\partial x)((x^2+x-y)^7) is 7(x^2+x-y)^6(2x+1)