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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (5 + 2 x) = 2

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

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

Simplify

2 e^{- 3 x} + (- 3 e^{- 3 x}) (5 + 2 x) : - 13 e^{- 3 x} - 6 e^{- 3 x} x

= - 13 e^{- 3 x} - 6 e^{- 3 x} x

Popular Examples

derivative of 2*e^{2x}

\frac{d}{d x} (2 \cdot e^{2 x})

integral from 3 to 4 of 1/(sin(x))

\int_{3}^{4} \frac{1}{sin ( x )} d x

laplacetransform 5cos(2t)-3sin(3t)laplace transform

5 cos (2 t) - 3 sin (3 t)

y^{''}-6/x y^'+(10)/(x^2)y=0

y^{^{''}} - \frac{6}{x} y^{^{'}} + \frac{10}{x ^{2}} y = 0

limit as h approaches 0 of (sqrt(h+5)-sqrt(5))/h

h \to 0 lim (\frac{h + 5 - 5}{h})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(5+2x)e^{-3x} ?
The derivative of f(x)=(5+2x)e^{-3x} is -13e^{-3x}-6e^{-3x}x
What is the first derivative of f(x)=(5+2x)e^{-3x} ?
The first derivative of f(x)=(5+2x)e^{-3x} is -13e^{-3x}-6e^{-3x}x