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Popular >

derivative of te^{4t}

Solution

derivative of

t e^{4 t}

Solution

e^{4 t} + 4 e^{4 t} t

Solution steps

\frac{d}{d t} (t e^{4 t})

Apply the Product Rule:

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

f = t, g = e^{4 t}

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

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

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

= 1 \cdot e^{4 t} + e^{4 t} \cdot 4 t

Simplify

= e^{4 t} + 4 e^{4 t} t

Popular Examples

derivative of axsin(x+bxcos(x))

\frac{d}{d x} (a x sin (x) + b x cos (x))

integral of e^{8x-7}

\int e^{8 x - 7} d x

integral of x^2*sqrt(7x-5)

\int x^{2} \cdot 7 x - 5 d x

integral of 5/(xsqrt(36-25ln^2(x)))

\int \frac{5}{x 36 - 25 ln ^{2} ( x )} d x

(\partial)/(\partial x)(ln(y^{x^2}))

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

Frequently Asked Questions (FAQ)

What is the derivative of te^{4t} ?
The derivative of te^{4t} is e^{4t}+4e^{4t}t
What is the first derivative of te^{4t} ?
The first derivative of te^{4t} is e^{4t}+4e^{4t}t