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Popular >

d/(dt)(Ate^{-4t})

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = t, g = e^{- 4 t}

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

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

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

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

Simplify

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

Popular Examples

integral from 2 to 3 of (12)/(sqrt(3-x))

\int_{2}^{3} \frac{12}{3 - x} d x

integral of (sqrt(x))/(x^3+1)

\int \frac{x}{x ^{3} + 1} d x

limit as x approaches 0 of (3^x-10^x)/x

x \to 0 lim (\frac{3 ^{x} - 1 0 ^{x}}{x})

integral from 0 to 1 of 7/(1+x^2)

\int_{0}^{1} \frac{7}{1 + x ^{2}} d x

integral of 2sin(1/2 x)

\int 2 sin (\frac{1}{2} x) d x

Frequently Asked Questions (FAQ)

What is the d/(dt)(Ate^{-4t}) ?
The d/(dt)(Ate^{-4t}) is A(e^{-4t}-4e^{-4t}t)
What is the first d/(dt)(Ate^{-4t}) ?
The first d/(dt)(Ate^{-4t}) is A(e^{-4t}-4e^{-4t}t)