What is the derivative of y=xe^{ax} ?

The derivative of y=xe^{ax} is e^{ax}+ae^{ax}x

What is the first derivative of y=xe^{ax} ?

The first derivative of y=xe^{ax} is e^{ax}+ae^{ax}x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = x e^{a x}

e^{a x} + a e^{a x} x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 1 \cdot e^{a x} + e^{a x} a x

Simplify

= e^{a x} + a e^{a x} x

\frac{d}{d x} (\frac{x ^{4}}{2} - \frac{3}{2} x^{2} - x)

x \to - 2 lim (x^{2} - 5)

\int_{1}^{\infty} x^{- \frac{4}{5}} d x

f^{^{'}} (x) = 6 x

f (x) = \frac{2}{3 x}

What is the derivative of y=xe^{ax} ?
The derivative of y=xe^{ax} is e^{ax}+ae^{ax}x
What is the first derivative of y=xe^{ax} ?
The first derivative of y=xe^{ax} is e^{ax}+ae^{ax}x