What is the derivative of e^{2x}cos(5x) ?

The derivative of e^{2x}cos(5x) is 2e^{2x}cos(5x)-5e^{2x}sin(5x)

What is the first derivative of e^{2x}cos(5x) ?

The first derivative of e^{2x}cos(5x) is 2e^{2x}cos(5x)-5e^{2x}sin(5x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

e^{2 x} cos (5 x)

2 e^{2 x} cos (5 x) - 5 e^{2 x} sin (5 x)

Solution steps

\frac{d}{d x} (e^{2 x} cos (5 x))

Apply the Product Rule:

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

f = e^{2 x}, g = cos (5 x)

= \frac{d}{d x} (e^{2 x}) cos (5 x) + \frac{d}{d x} (cos (5 x)) e^{2 x}

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

\frac{d}{d x} (cos (5 x)) = - sin (5 x) \cdot 5

= e^{2 x} \cdot 2 cos (5 x) + (- sin (5 x) \cdot 5) e^{2 x}

Simplify

= 2 e^{2 x} cos (5 x) - 5 e^{2 x} sin (5 x)

f (x) = \frac{6 x}{3 + x}

\frac{d}{d x} (144 - x^{2})

1 + x

x y^{^{'}} - y = \frac{2}{3} x ln (x)

x^{2.4} + e^{2.4}

What is the derivative of e^{2x}cos(5x) ?
The derivative of e^{2x}cos(5x) is 2e^{2x}cos(5x)-5e^{2x}sin(5x)
What is the first derivative of e^{2x}cos(5x) ?
The first derivative of e^{2x}cos(5x) is 2e^{2x}cos(5x)-5e^{2x}sin(5x)