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Popular >

derivative of 4te^{-t}

Solution

derivative of

4 t e^{- t}

Solution

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)

Popular Examples

limit as x approaches-1 of 1+e^{1/x}

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

integral from 2 to 4 of (-x^2+6x-8)

\int_{2}^{4} (- x^{2} + 6 x - 8) d x

derivative of x^3(8x^2+2x-3^2)

\frac{d}{d x} (x^{3} (8 x^{2} + 2 x - 3)^{2})

limit as x approaches+0 of (2x+1)/(x^3)

x \to + 0 lim (\frac{2 x + 1}{x ^{3}})

(\partial)/(\partial y)(xye^{-3y})

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

Frequently Asked Questions (FAQ)

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)