What is (\partial)/(\partial x)((2+3x)(3-2x)) ?

The answer to (\partial)/(\partial x)((2+3x)(3-2x)) is -12x+5

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(\partial)/(\partial x)((2+3x)(3-2x))

\frac{\partial}{\partial x} ((2 + 3 x) (3 - 2 x))

- 12 x + 5

Solution steps

\frac{\partial}{\partial x} ((2 + 3 x) (3 - 2 x))

Apply the Product Rule:

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

f = 2 + 3 x, g = 3 - 2 x

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

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

\frac{\partial}{\partial x} (3 - 2 x) = - 2

= 3 (3 - 2 x) + (- 2) (2 + 3 x)

Simplify

3 (3 - 2 x) + (- 2) (2 + 3 x) : - 12 x + 5

= - 12 x + 5

y^{^{'}} = \frac{( x - y )}{( x + 2 y )}

\int \frac{1}{x ^{2}} ln (x) d x

\frac{d}{d y} (\frac{ln ( y )}{2 y} + \frac{1}{y})

x \to - 2 lim (- 10)

x y^{^{'}} + y = y^{2}, y (1) = - 9

What is (\partial)/(\partial x)((2+3x)(3-2x)) ?
The answer to (\partial)/(\partial x)((2+3x)(3-2x)) is -12x+5