en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=(3+2x)e^{-3x}

Solution

derivative of

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

Solution

- 7 e^{- 3 x} - 6 e^{- 3 x} x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 e^{- 3 x} + (- 3 e^{- 3 x}) (3 + 2 x) : - 7 e^{- 3 x} - 6 e^{- 3 x} x

= - 7 e^{- 3 x} - 6 e^{- 3 x} x

Popular Examples

integral from 0 to 2 of (3x^2-6x+1)

\int_{0}^{2} (3 x^{2} - 6 x + 1) d x

derivative of y=x^2-2x-24sqrt(x)derivative of

y = x^{2} - 2 x - 24 x

y^'=-x/y+((x^2+y^2))/y ,y(0)=-1

y^{^{'}} = - \frac{x}{y} + \frac{( x ^{2} + y ^{2} )}{y}, y (0) = - 1

integral of cos(x)(3+5sin^2(x))

\int cos (x) (3 + 5 sin^{2} (x)) d x

integral of (2x+1)/((x+7)^2)

\int \frac{2 x + 1}{( x + 7 ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(3+2x)e^{-3x} ?
The derivative of f(x)=(3+2x)e^{-3x} is -7e^{-3x}-6e^{-3x}x
What is the first derivative of f(x)=(3+2x)e^{-3x} ?
The first derivative of f(x)=(3+2x)e^{-3x} is -7e^{-3x}-6e^{-3x}x