What is (\partial)/(\partial x)((3x+4y)^5) ?

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

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(\partial)/(\partial x)((3x+4y)^5)

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

y = \frac{x ^{5}}{1 - x ^{4}}

x \to \infty lim (sin (0))

n = 2 \sum \infty \frac{ln ( n )}{7 n}

n = 0 \sum \infty \frac{2 n}{n ^{2} + 1}

\frac{x}{x ^{2} + 4}

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