What is (\partial)/(\partial x)((3x+5)(2x+6y)) ?

The answer to (\partial)/(\partial x)((3x+5)(2x+6y)) is 12x+18y+10

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(\partial)/(\partial x)((3x+5)(2x+6y))

\frac{\partial}{\partial x} ((3 x + 5) (2 x + 6 y))

12 x + 18 y + 10

Solution steps

\frac{\partial}{\partial x} ((3 x + 5) (2 x + 6 y))

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 3 x + 5, g = 2 x + 6 y

= \frac{\partial}{\partial x} (3 x + 5) (2 x + 6 y) + \frac{\partial}{\partial x} (2 x + 6 y) (3 x + 5)

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

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

= 3 (2 x + 6 y) + 2 (3 x + 5)

Simplify

3 (2 x + 6 y) + 2 (3 x + 5) : 12 x + 18 y + 10

= 12 x + 18 y + 10

\int x \cdot e^{- x} d x

\frac{\partial}{\partial x} (x^{0.5} \cdot y)

x \to 0 lim (csc (x))

\int x^{2} 4 x + 4 d x

cos (3 t) sin (2 t)

What is (\partial)/(\partial x)((3x+5)(2x+6y)) ?
The answer to (\partial)/(\partial x)((3x+5)(2x+6y)) is 12x+18y+10