What is (\partial)/(\partial x)((3x^2+3x-1)(2x+3)) ?

The answer to (\partial)/(\partial x)((3x^2+3x-1)(2x+3)) is 18x^2+30x+7

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(\partial)/(\partial x)((3x^2+3x-1)(2x+3))

\frac{\partial}{\partial x} ((3 x^{2} + 3 x - 1) (2 x + 3))

18 x^{2} + 30 x + 7

Solution steps

\frac{\partial}{\partial x} ((3 x^{2} + 3 x - 1) (2 x + 3))

Apply the Product Rule:

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

f = 3 x^{2} + 3 x - 1, g = 2 x + 3

= \frac{\partial}{\partial x} (3 x^{2} + 3 x - 1) (2 x + 3) + \frac{\partial}{\partial x} (2 x + 3) (3 x^{2} + 3 x - 1)

\frac{\partial}{\partial x} (3 x^{2} + 3 x - 1) = 6 x + 3

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

= (6 x + 3) (2 x + 3) + 2 (3 x^{2} + 3 x - 1)

Simplify

(6 x + 3) (2 x + 3) + 2 (3 x^{2} + 3 x - 1) : 18 x^{2} + 30 x + 7

= 18 x^{2} + 30 x + 7

y = (x + 5) (3 x + 8)

\int \frac{( x + 1 )}{( x ^{2} + 2 x + 2 ) ^{3}} d x

\frac{d y}{d x} = 1 + \frac{y}{x}

y = lo g_{4} (x) + lo g_{4} (x^{2})

\frac{d}{d x} (x^{2} - 8)

What is (\partial)/(\partial x)((3x^2+3x-1)(2x+3)) ?
The answer to (\partial)/(\partial x)((3x^2+3x-1)(2x+3)) is 18x^2+30x+7