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

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

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

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

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derivative of

f (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

\int_{1}^{5} (x^{2} - x + 1) d x

\frac{d}{d x} (- sin (4 x))

y = e^{x^{4}}

\frac{d y}{d x} = (1 + e^{2 x})

\frac{d}{d x} (\frac{x ^{2}}{x - 9})

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