What is the derivative of 5te^{-t/7} ?

The derivative of 5te^{-t/7} is 5(e^{-t/7}-(e^{-t/7}t)/7)

What is the first derivative of 5te^{-t/7} ?

The first derivative of 5te^{-t/7} is 5(e^{-t/7}-(e^{-t/7}t)/7)

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derivative of

5 t e^{- \frac{t}{7}}

5 (e^{- \frac{t}{7}} - \frac{e ^{- \frac{t}{7}} t}{7})

Solution steps

\frac{d}{d t} (5 t e^{- \frac{t}{7}})

Take the constant out:

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

= 5 \frac{d}{d t} (t e^{- \frac{t}{7}})

Apply the Product Rule:

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

f = t, g = e^{- \frac{t}{7}}

= 5 (\frac{d t}{d t} e^{- \frac{t}{7}} + \frac{d}{d t} (e^{- \frac{t}{7}}) t)

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

\frac{d}{d t} (e^{- \frac{t}{7}}) = - \frac{1}{7} e^{- \frac{t}{7}}

= 5 (1 \cdot e^{- \frac{t}{7}} + (- \frac{1}{7} e^{- \frac{t}{7}}) t)

Simplify

5 (1 \cdot e^{- \frac{t}{7}} + (- \frac{1}{7} e^{- \frac{t}{7}}) t) : 5 (e^{- \frac{t}{7}} - \frac{e ^{- \frac{t}{7}} t}{7})

= 5 (e^{- \frac{t}{7}} - \frac{e ^{- \frac{t}{7}} t}{7})

\frac{\partial}{\partial x} (e^{- x^{8} - y^{4}})

\int 6 sin^{3} (6 x) cos^{3} (6 x) d x

x \to \infty + lim (3 e^{x})

\int 7 cos^{3} (4 x) d x

t^{2} y^{^{'}} + y = sin (t), y (1) = 0

What is the derivative of 5te^{-t/7} ?
The derivative of 5te^{-t/7} is 5(e^{-t/7}-(e^{-t/7}t)/7)
What is the first derivative of 5te^{-t/7} ?
The first derivative of 5te^{-t/7} is 5(e^{-t/7}-(e^{-t/7}t)/7)