What is (\partial)/(\partial x)((x^2+5xy-2y)^8) ?

The answer to (\partial)/(\partial x)((x^2+5xy-2y)^8) is 8(x^2+5xy-2y)^7(2x+5y)

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(\partial)/(\partial x)((x^2+5xy-2y)^8)

\frac{\partial}{\partial x} ((x^{2} + 5 x y - 2 y)^{8})

8 (x^{2} + 5 x y - 2 y)^{7} (2 x + 5 y)

Solution steps

\frac{\partial}{\partial x} ((x^{2} + 5 x y - 2 y)^{8})

Treat

y

as a constant

Apply the chain rule:

8 (x^{2} + 5 x y - 2 y)^{7} \frac{\partial}{\partial x} (x^{2} + 5 x y - 2 y)

= 8 (x^{2} + 5 x y - 2 y)^{7} \frac{\partial}{\partial x} (x^{2} + 5 x y - 2 y)

\frac{\partial}{\partial x} (x^{2} + 5 x y - 2 y) = 2 x + 5 y

= 8 (x^{2} + 5 x y - 2 y)^{7} (2 x + 5 y)

e^{- 5 t} sin (7 t)

\frac{d}{d x} (arctan (2 x^{3}))

\int \frac{( 5 x + 7 )}{x ^{2} + 4 x + 4} d x

\frac{d}{d x} (10000 - 9000 e^{- 0.3 x})

What is (\partial)/(\partial x)((x^2+5xy-2y)^8) ?
The answer to (\partial)/(\partial x)((x^2+5xy-2y)^8) is 8(x^2+5xy-2y)^7(2x+5y)