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Popular >

d/(dt)(te^{t^3})

Solution

\frac{d}{d t} (t e^{t^{3}})

Solution

e^{t^{3}} + 3 e^{t^{3}} t^{3}

Solution steps

\frac{d}{d t} (t e^{t^{3}})

Apply the Product Rule:

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

f = t, g = e^{t^{3}}

= \frac{d t}{d t} e^{t^{3}} + \frac{d}{d t} (e^{t^{3}}) t

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

\frac{d}{d t} (e^{t^{3}}) = e^{t^{3}} \cdot 3 t^{2}

= 1 \cdot e^{t^{3}} + e^{t^{3}} \cdot 3 t^{2} t

Simplify

1 \cdot e^{t^{3}} + e^{t^{3}} \cdot 3 t^{2} t : e^{t^{3}} + 3 e^{t^{3}} t^{3}

= e^{t^{3}} + 3 e^{t^{3}} t^{3}

Graph

Popular Examples

integral from 3 to 6 of (x^2)

\int_{3}^{6} (x^{2}) d x

integral from-4 to-6 of (-2)^{-3}

\int_{- 4}^{- 6} (- 2)^{- 3} d x

integral from 0 to pi of sin(2x)

\int_{0}^{π} sin (2 x) d x

integral of 1/((x^2+7))

\int \frac{1}{( x ^{2} + 7 )} d x

slope of y=sqrt(1-4x),\at x=-1 slope

y = 1 - 4 x, at x = - 1

Frequently Asked Questions (FAQ)

What is the d/(dt)(te^{t^3}) ?
The d/(dt)(te^{t^3}) is e^{t^3}+3e^{t^3}t^3
What is the first d/(dt)(te^{t^3}) ?
The first d/(dt)(te^{t^3}) is e^{t^3}+3e^{t^3}t^3