en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(t)=e^{5tsin(2t)}

Solution

derivative of

f (t) = e^{5 t s i n (2 t)}

Solution

e^{5 t s i n (2 t)} \cdot 5 (sin (2 t) + 2 t cos (2 t))

Solution steps

\frac{d}{d t} (e^{5 t s i n (2 t)})

Apply the chain rule:

e^{5 t s i n (2 t)} \frac{d}{d t} (5 t sin (2 t))

= e^{5 t s i n (2 t)} \frac{d}{d t} (5 t sin (2 t))

\frac{d}{d t} (5 t sin (2 t)) = 5 (sin (2 t) + 2 t cos (2 t))

= e^{5 t s i n (2 t)} \cdot 5 (sin (2 t) + 2 t cos (2 t))

Popular Examples

derivative of 15(cos(x)-xsin(x))derivative of

15 (cos (x) - x sin (x))

limit as x approaches 1-of 6/(x^3-1)

x \to 1 - lim (\frac{6}{x ^{3} - 1})

limit as x approaches 0+of tan^x(2x)

x \to 0 + lim (tan^{x} (2 x))

(\partial)/(\partial z)(2ze^{xyz})

\frac{\partial}{\partial z} (2 z e^{x yz})

9y^{''}+48y^'+64y=0

9 y^{^{''}} + 48 y^{^{'}} + 64 y = 0

Frequently Asked Questions (FAQ)

What is the derivative of f(t)=e^{5tsin(2t)} ?
The derivative of f(t)=e^{5tsin(2t)} is e^{5tsin(2t)}*5(sin(2t)+2tcos(2t))
What is the first derivative of f(t)=e^{5tsin(2t)} ?
The first derivative of f(t)=e^{5tsin(2t)} is e^{5tsin(2t)}*5(sin(2t)+2tcos(2t))