en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

d/(dt)(4e^tsin(t))

Solution

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

Solution

4 (e^{t} sin (t) + cos (t) e^{t})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = e^{t}, g = sin (t)

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

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

\frac{d}{d t} (sin (t)) = cos (t)

= 4 (e^{t} sin (t) + cos (t) e^{t})

Graph

Popular Examples

integral of (5/x-3/(x^2))

\int (\frac{5}{x} - \frac{3}{x ^{2}}) d x

integral from 5 to 8 of 6/(sqrt(x-5))

\int_{5}^{8} \frac{6}{x - 5} d x

t^2y^'+y^2=ty,y(1)=-1/2

t^{2} y^{^{'}} + y^{2} = t y, y (1) = - \frac{1}{2}

(\partial)/(\partial x)(ln(x-y^2))

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

(dy)/(dx)=(4sec(y))/((x-6)^2)

\frac{d y}{d x} = \frac{4 sec ( y )}{( x - 6 ) ^{2}}

Frequently Asked Questions (FAQ)

What is the d/(dt)(4e^tsin(t)) ?
The d/(dt)(4e^tsin(t)) is 4(e^tsin(t)+cos(t)e^t)
What is the first d/(dt)(4e^tsin(t)) ?
The first d/(dt)(4e^tsin(t)) is 4(e^tsin(t)+cos(t)e^t)