What is (\partial)/(\partial x)((7x+3y)^5) ?

The answer to (\partial)/(\partial x)((7x+3y)^5) is 35(7x+3y)^4

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(\partial)/(\partial x)((7x+3y)^5)

\frac{\partial}{\partial x} ((7 x + 3 y)^{5})

35 (7 x + 3 y)^{4}

Solution steps

\frac{\partial}{\partial x} ((7 x + 3 y)^{5})

Treat

y

as a constant

Apply the chain rule:

5 (7 x + 3 y)^{4} \frac{\partial}{\partial x} (7 x + 3 y)

= 5 (7 x + 3 y)^{4} \frac{\partial}{\partial x} (7 x + 3 y)

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

= 5 (7 x + 3 y)^{4} \cdot 7

Simplify

= 35 (7 x + 3 y)^{4}

\frac{\partial}{\partial y} ((- x^{4} + 7 y^{2} + 3 y)^{6})

\frac{d}{d x} (x^{2} - 2 y)

\frac{d y}{d x} = 7 x cos^{2} (y)

\frac{d}{d x} (\frac{1}{2 x + 8})

y^{^{''}} - 8 y^{^{'}} + 15 y = 2 e^{3 x}

What is (\partial)/(\partial x)((7x+3y)^5) ?
The answer to (\partial)/(\partial x)((7x+3y)^5) is 35(7x+3y)^4