en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

d/(dt)(7e^tsin(t))

Solution

\frac{d}{d t} (7 e^{t} sin (t))

Solution

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

Solution steps

\frac{d}{d t} (7 e^{t} sin (t))

Take the constant out:

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

= 7 \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)

= 7 (\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)

= 7 (e^{t} sin (t) + cos (t) e^{t})

Graph

Popular Examples

derivative of (2x^2/(x^2+1))

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

derivative of 1+4/x

\frac{d}{d x} (1 + \frac{4}{x})

integral of (ln(3x+1))/(6x+2)

\int \frac{ln ( 3 x + 1 )}{6 x + 2} d x

derivative of 6+1/8 (t-4)^2 derivative of

6 + \frac{1}{8} (t - 4)^{2}

integral of pitcos(nt)

\int π t cos (n t) d t

Frequently Asked Questions (FAQ)

What is the d/(dt)(7e^tsin(t)) ?
The d/(dt)(7e^tsin(t)) is 7(e^tsin(t)+cos(t)e^t)
What is the first d/(dt)(7e^tsin(t)) ?
The first d/(dt)(7e^tsin(t)) is 7(e^tsin(t)+cos(t)e^t)