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Popular >

derivative of te^{-t^5}

Solution

derivative of

t e^{- t^{5}}

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d t} (e^{- t^{5}}) = - 5 e^{- t^{5}} t^{4}

= 1 \cdot e^{- t^{5}} + (- 5 e^{- t^{5}} t^{4}) t

Simplify

1 \cdot e^{- t^{5}} + (- 5 e^{- t^{5}} t^{4}) t : e^{- t^{5}} - 5 e^{- t^{5}} t^{5}

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

Popular Examples

(\partial)/(\partial x)((xy)^2)

\frac{\partial}{\partial x} ((x y)^{2})

derivative of 1/(x^1)

\frac{d}{d x} (\frac{1}{x ^{1}})

derivative of xex

\frac{d}{d x} (x e x)

y^{''}-2y^'+5y=17cos(2x)

y^{^{''}} - 2 y^{^{'}} + 5 y = 17 cos (2 x)

integral of x(12x+8)

\int x (12 x + 8) d x

Frequently Asked Questions (FAQ)

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