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Popular >

d/(dt)(2te^{-t})

Solution

\frac{d}{d t} (2 t e^{- t})

Solution

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

Solution steps

\frac{d}{d t} (2 t e^{- t})

Take the constant out:

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

= 2 \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}

= 2 (\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}

= 2 (1 \cdot e^{- t} + (- e^{- t}) t)

Simplify

= 2 (e^{- t} - e^{- t} t)

Popular Examples

integral of 1/(sin(x)cos^2(x))

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

tangent of f(x)=10sin(x)+10sqrt(3)cos(x)tangent of

f (x) = 10 sin (x) + 103 cos (x)

inverse oflaplace 2/(s^2+3s+2)inverse laplace

\frac{2}{s ^{2} + 3 s + 2}

sum from n=5 to infinity of (n^2)/(n!)

n = 5 \sum \infty \frac{n ^{2}}{n !}

integral from-1 to 1 of sqrt(1+x^{-2/3)}

\int_{- 1}^{1} 1 + x^{- \frac{2}{3}} d x

Frequently Asked Questions (FAQ)

What is the d/(dt)(2te^{-t}) ?
The d/(dt)(2te^{-t}) is 2(e^{-t}-e^{-t}t)
What is the first d/(dt)(2te^{-t}) ?
The first d/(dt)(2te^{-t}) is 2(e^{-t}-e^{-t}t)