en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ax*e^{bx}

Solution

\frac{d}{d x} (a x \cdot e^{b x})

Solution

a (e^{b x} + b e^{b x} x)

Solution steps

\frac{d}{d x} (a x e^{b x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= a \frac{d}{d x} (x e^{b x})

Apply the Product Rule:

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

f = x, g = e^{b x}

= a (\frac{d x}{d x} e^{b x} + \frac{d}{d x} (e^{b x}) x)

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

\frac{d}{d x} (e^{b x}) = e^{b x} b

= a (1 \cdot e^{b x} + e^{b x} b x)

Simplify

= a (e^{b x} + b e^{b x} x)

Popular Examples

tangent of f(x)=(11x-1)^{-1/5},\at x=3 tangent of

f (x) = (11 x - 1)^{- \frac{1}{5}}, at x = 3

(\partial)/(\partial x)((-y)/(x^2+y^2))

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

derivative of ln((2x+3^2))

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

derivative of x^{-9cos(x)}derivative of

x^{- 9 c o s (x)}

derivative of log_{e}(5x)

\frac{d}{d x} (lo g_{e} (5 x))

Frequently Asked Questions (FAQ)

What is the derivative of ax*e^{bx} ?
The derivative of ax*e^{bx} is a(e^{bx}+be^{bx}x)
What is the first derivative of ax*e^{bx} ?
The first derivative of ax*e^{bx} is a(e^{bx}+be^{bx}x)