What is the derivative of (3-5xe^x(3x+2)) ?

The derivative of (3-5xe^x(3x+2)) is -15e^xx^2-40e^xx-10e^x+9

What is the first derivative of (3-5xe^x(3x+2)) ?

The first derivative of (3-5xe^x(3x+2)) is -15e^xx^2-40e^xx-10e^x+9

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\frac{d}{d x} ((3 - 5 x e^{x}) (3 x + 2))

- 15 e^{x} x^{2} - 40 e^{x} x - 10 e^{x} + 9

Solution steps

\frac{d}{d x} ((3 - 5 x e^{x}) (3 x + 2))

Apply the Product Rule:

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

f = 3 - 5 x e^{x}, g = 3 x + 2

= \frac{d}{d x} (3 - 5 x e^{x}) (3 x + 2) + \frac{d}{d x} (3 x + 2) (3 - 5 x e^{x})

\frac{d}{d x} (3 - 5 x e^{x}) = - 5 (e^{x} x + e^{x})

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

= (- 5 (e^{x} x + e^{x})) (3 x + 2) + 3 (3 - 5 x e^{x})

Simplify

(- 5 (e^{x} x + e^{x})) (3 x + 2) + 3 (3 - 5 x e^{x}) : - 15 e^{x} x^{2} - 40 e^{x} x - 10 e^{x} + 9

= - 15 e^{x} x^{2} - 40 e^{x} x - 10 e^{x} + 9

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What is the derivative of (3-5xe^x(3x+2)) ?
The derivative of (3-5xe^x(3x+2)) is -15e^xx^2-40e^xx-10e^x+9
What is the first derivative of (3-5xe^x(3x+2)) ?
The first derivative of (3-5xe^x(3x+2)) is -15e^xx^2-40e^xx-10e^x+9