en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of e^{ax}cos(bx)

Solution

\frac{d}{d x} (e^{a x} cos (b x))

Solution

a e^{a x} cos (b x) - b e^{a x} sin (b x)

Solution steps

\frac{d}{d x} (e^{a x} cos (b x))

Apply the Product Rule:

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

f = e^{a x}, g = cos (b x)

= \frac{d}{d x} (e^{a x}) cos (b x) + \frac{d}{d x} (cos (b x)) e^{a x}

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

\frac{d}{d x} (cos (b x)) = - sin (b x) b

= e^{a x} a cos (b x) + (- sin (b x) b) e^{a x}

Simplify

= a e^{a x} cos (b x) - b e^{a x} sin (b x)

Popular Examples

integral from 1 to 2 of ((3x-1))/(3x)

\int_{1}^{2} \frac{( 3 x - 1 )}{3 x} d x

derivative of sin(5xe^{3x})

\frac{d}{d x} (sin (5 x) e^{3 x})

2 y^{^{'}} + 3 y = 0

(\partial)/(\partial x)(2/(2x-2z+1))

\frac{\partial}{\partial x} (\frac{2}{2 x - 2 z + 1})

derivative of x*sqrt(3x^2+5)derivative of

x \cdot 3 x^{2} + 5

Frequently Asked Questions (FAQ)

What is the derivative of e^{ax}cos(bx) ?
The derivative of e^{ax}cos(bx) is ae^{ax}cos(bx)-be^{ax}sin(bx)
What is the first derivative of e^{ax}cos(bx) ?
The first derivative of e^{ax}cos(bx) is ae^{ax}cos(bx)-be^{ax}sin(bx)