What is (\partial)/(\partial x)((2x+3y)^7) ?

The answer to (\partial)/(\partial x)((2x+3y)^7) is 14(2x+3y)^6

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(\partial)/(\partial x)((2x+3y)^7)

\frac{\partial}{\partial x} ((2 x + 3 y)^{7})

14 (2 x + 3 y)^{6}

Solution steps

\frac{\partial}{\partial x} ((2 x + 3 y)^{7})

Treat

y

as a constant

Apply the chain rule:

7 (2 x + 3 y)^{6} \frac{\partial}{\partial x} (2 x + 3 y)

= 7 (2 x + 3 y)^{6} \frac{\partial}{\partial x} (2 x + 3 y)

\frac{\partial}{\partial x} (2 x + 3 y) = 2

= 7 (2 x + 3 y)^{6} \cdot 2

Simplify

= 14 (2 x + 3 y)^{6}

\frac{d}{d x} (- 16 x^{2} + 64 x)

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\int \frac{3 x + 5}{x ^{2} + 2 x + 10} d x

\int x e n (x) d x

\int (x + \frac{1}{7 x}) d x

What is (\partial)/(\partial x)((2x+3y)^7) ?
The answer to (\partial)/(\partial x)((2x+3y)^7) is 14(2x+3y)^6