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Popular >

derivative of f(t)=te^{5-2t}

Solution

derivative of

f (t) = t e^{5 - 2 t}

Solution

e^{5 - 2 t} - 2 e^{5 - 2 t} t

Solution steps

\frac{d}{d t} (t e^{5 - 2 t})

Apply the Product Rule:

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

f = t, g = e^{5 - 2 t}

= \frac{d t}{d t} e^{5 - 2 t} + \frac{d}{d t} (e^{5 - 2 t}) t

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

\frac{d}{d t} (e^{5 - 2 t}) = - 2 e^{5 - 2 t}

= 1 \cdot e^{5 - 2 t} + (- 2 e^{5 - 2 t}) t

Simplify

= e^{5 - 2 t} - 2 e^{5 - 2 t} t

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\frac{\partial}{\partial x} (x^{4} + 2 x y^{9})

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Frequently Asked Questions (FAQ)

What is the derivative of f(t)=te^{5-2t} ?
The derivative of f(t)=te^{5-2t} is e^{5-2t}-2e^{5-2t}t
What is the first derivative of f(t)=te^{5-2t} ?
The first derivative of f(t)=te^{5-2t} is e^{5-2t}-2e^{5-2t}t