What is the derivative of 2t^2e^{-t} ?

The derivative of 2t^2e^{-t} is 2(2e^{-t}t-e^{-t}t^2)

What is the first derivative of 2t^2e^{-t} ?

The first derivative of 2t^2e^{-t} is 2(2e^{-t}t-e^{-t}t^2)

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derivative of

2 t^{2} e^{- t}

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = t^{2}, g = e^{- t}

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

\frac{d}{d t} (t^{2}) = 2 t

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

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

Simplify

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

\frac{( x ^{2} + 1 )}{( 1 - x )}

\frac{d}{d t} (30 + 2 t)

y = 3 cos^{4} (x)

3 q^{2}

\frac{d}{d x} ((x^{2} + y^{2} + z^{2})^{3})

What is the derivative of 2t^2e^{-t} ?
The derivative of 2t^2e^{-t} is 2(2e^{-t}t-e^{-t}t^2)
What is the first derivative of 2t^2e^{-t} ?
The first derivative of 2t^2e^{-t} is 2(2e^{-t}t-e^{-t}t^2)