en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of e^{3x}cos(3x)

Solution

\frac{d}{d x} (e^{3 x} cos (3 x))

Solution

3 e^{3 x} cos (3 x) - 3 e^{3 x} sin (3 x)

Solution steps

\frac{d}{d x} (e^{3 x} cos (3 x))

Apply the Product Rule:

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

f = e^{3 x}, g = cos (3 x)

= \frac{d}{d x} (e^{3 x}) cos (3 x) + \frac{d}{d x} (cos (3 x)) e^{3 x}

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= e^{3 x} \cdot 3 cos (3 x) + (- sin (3 x) \cdot 3) e^{3 x}

Simplify

= 3 e^{3 x} cos (3 x) - 3 e^{3 x} sin (3 x)

Graph

Popular Examples

integral of 19sin^2(xco)s^2x

\int 19 sin^{2} (x co) s^{2} x d x

integral from-pi to pi of sin(3x)sin(3x)

\int_{- π}^{π} sin (3 x) sin (3 x) d x

derivative of y= 1/3 x^{3/2}

d er i v a t i v e y = \frac{1}{3} x^{\frac{3}{2}}

(\partial)/(\partial x)(2x^2+2y^2)

\frac{\partial}{\partial x} (2 x^{2} + 2 y^{2})

derivative of x/(sqrt(9-4x))

\frac{d}{d x} (\frac{x}{9 - 4 x})

Frequently Asked Questions (FAQ)

What is the derivative of e^{3x}cos(3x) ?
The derivative of e^{3x}cos(3x) is 3e^{3x}cos(3x)-3e^{3x}sin(3x)
What is the first derivative of e^{3x}cos(3x) ?
The first derivative of e^{3x}cos(3x) is 3e^{3x}cos(3x)-3e^{3x}sin(3x)