en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of e^xsin(9x)

Solution

\frac{d}{d x} (e^{x} sin (9 x))

Solution

e^{x} sin (9 x) + cos (9 x) \cdot 9 e^{x}

Solution steps

\frac{d}{d x} (e^{x} sin (9 x))

Apply the Product Rule:

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

f = e^{x}, g = sin (9 x)

= \frac{d}{d x} (e^{x}) sin (9 x) + \frac{d}{d x} (sin (9 x)) e^{x}

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

\frac{d}{d x} (sin (9 x)) = cos (9 x) \cdot 9

= e^{x} sin (9 x) + cos (9 x) \cdot 9 e^{x}

Popular Examples

derivative of e^{-2x}+1/3 e^x derivative of

e^{- 2 x} + \frac{1}{3} e^{x}

limit as x approaches infinity of 0x

x \to \infty lim (0 x)

inverse oflaplace 1/(5s+1)inverse laplace

\frac{1}{5 s + 1}

integral of*10^{-3}+*10^{-5}t+*10^{-8}t^2+*10^{-12}t^3

\int \cdot 1 0^{- 3} + \cdot 1 0^{- 5} t + \cdot 1 0^{- 8} t^{2} + \cdot 1 0^{- 12} t^{3} d t

integral of (9x^2+25)((7x-4)/(x^2))

\int (9 x^{2} + 25) (\frac{7 x - 4}{x ^{2}}) d x

Frequently Asked Questions (FAQ)

What is the derivative of e^xsin(9x) ?
The derivative of e^xsin(9x) is e^xsin(9x)+cos(9x)*9e^x
What is the first derivative of e^xsin(9x) ?
The first derivative of e^xsin(9x) is e^xsin(9x)+cos(9x)*9e^x