What is the derivative of 4te^{-t} ?

The derivative of 4te^{-t} is 4(e^{-t}-e^{-t}t)

What is the first derivative of 4te^{-t} ?

The first derivative of 4te^{-t} is 4(e^{-t}-e^{-t}t)

derivative of

4 t e^{- t}

4 (e^{- t} - e^{- t} t)

Solution steps

\frac{d}{d t} (4 t e^{- t})

Take the constant out:

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

= 4 \frac{d}{d t} (t e^{- t})

Apply the Product Rule:

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

f = t, g = e^{- t}

= 4 (\frac{d t}{d t} e^{- t} + \frac{d}{d t} (e^{- t}) t)

\frac{d t}{d t} = 1

\frac{d}{d t} (e^{- t}) = - e^{- t}

= 4 (1 \cdot e^{- t} + (- e^{- t}) t)

Simplify

= 4 (e^{- t} - e^{- t} t)

x \to - 1 lim (1 + e^{\frac{1}{x}})

a re a x^{2} - 3 x, 5 x, [0, 8]

\frac{d y}{d x} + y = 2 x y^{2} e x

\frac{d}{d x} (\frac{4 x - x ^{2}}{6 - x})

d er i v a t i v e e^{- x^{4}}

What is the derivative of 4te^{-t} ?
The derivative of 4te^{-t} is 4(e^{-t}-e^{-t}t)
What is the first derivative of 4te^{-t} ?
The first derivative of 4te^{-t} is 4(e^{-t}-e^{-t}t)