What is the derivative of ye^{-3x} ?

The derivative of ye^{-3x} is e^{-3x}(dy)/(dx)-3e^{-3x}y

What is the first derivative of ye^{-3x} ?

The first derivative of ye^{-3x} is e^{-3x}(dy)/(dx)-3e^{-3x}y

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

e^{- 3 x} \frac{d y}{d x} - 3 e^{- 3 x} y

Solution steps

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

Apply the Product Rule:

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

f = y, g = e^{- 3 x}

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

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

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

Simplify

= e^{- 3 x} \frac{d y}{d x} - 3 e^{- 3 x} y

x^{2} + x - 3

- t^{3} + 15 t^{2} - 72 t

\frac{\partial}{\partial y} (3 x^{2} + 4 y^{2})

x \to 0 lim (1 + cos^{3} (x))

y^{^{'}} \cdot 1 + x^{2} = x y^{2}

What is the derivative of ye^{-3x} ?
The derivative of ye^{-3x} is e^{-3x}(dy)/(dx)-3e^{-3x}y
What is the first derivative of ye^{-3x} ?
The first derivative of ye^{-3x} is e^{-3x}(dy)/(dx)-3e^{-3x}y