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

The derivative of y=te^{-t} is e^{-t}-e^{-t}t

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

The first derivative of y=te^{-t} is e^{-t}-e^{-t}t

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derivative of

y = t e^{- t}

e^{- t} - e^{- t} t

Solution steps

\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}

= \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}

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

Simplify

= e^{- t} - e^{- t} t

x y^{2} \frac{d y}{d x} = y^{3} - x^{3}, y (1) = 3

\int \frac{x}{2 x - 1} d x

y^{^{'}} = \frac{x}{10 y}

\int sec (x) tan^{5} (x) d x

\frac{\partial}{\partial x} (x + x y + y)

What is the derivative of y=te^{-t} ?
The derivative of y=te^{-t} is e^{-t}-e^{-t}t
What is the first derivative of y=te^{-t} ?
The first derivative of y=te^{-t} is e^{-t}-e^{-t}t