What is (\partial)/(\partial x)((3x+2y)^5) ?

The answer to (\partial)/(\partial x)((3x+2y)^5) is 15(3x+2y)^4

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(\partial)/(\partial x)((3x+2y)^5)

\frac{\partial}{\partial x} ((3 x + 2 y)^{5})

15 (3 x + 2 y)^{4}

Solution steps

\frac{\partial}{\partial x} ((3 x + 2 y)^{5})

Treat

y

as a constant

Apply the chain rule:

5 (3 x + 2 y)^{4} \frac{\partial}{\partial x} (3 x + 2 y)

= 5 (3 x + 2 y)^{4} \frac{\partial}{\partial x} (3 x + 2 y)

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

= 5 (3 x + 2 y)^{4} \cdot 3

Simplify

= 15 (3 x + 2 y)^{4}

x \to 4 lim (\frac{1}{x - 4})

\frac{d y}{d x} = 2 x - 3 y

4 e^{x} + 3 x e^{x}

4 (x + 2)^{\frac{3}{2}}

\frac{d}{d x} ((sin (x) + cos (x)) sec (x))

What is (\partial)/(\partial x)((3x+2y)^5) ?
The answer to (\partial)/(\partial x)((3x+2y)^5) is 15(3x+2y)^4