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

The derivative of e^{2x}+xe^{2x}+cos(2x) is 3e^{2x}+2e^{2x}x-2sin(2x)

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

The first derivative of e^{2x}+xe^{2x}+cos(2x) is 3e^{2x}+2e^{2x}x-2sin(2x)

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} + x e^{2 x} + cos (2 x)

3 e^{2 x} + 2 e^{2 x} x - 2 sin (2 x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

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

Simplify

= 3 e^{2 x} + 2 e^{2 x} x - 2 sin (2 x)

\frac{\partial}{\partial x} (ln (y cos (x)))

y = e^{x}, at x = ln (2)

\int x (2 x + 5)^{20} d x

\frac{\partial}{\partial x} (7 e^{x} sin (y))

x \to 2 lim (7 x - 4)

What is the derivative of e^{2x}+xe^{2x}+cos(2x) ?
The derivative of e^{2x}+xe^{2x}+cos(2x) is 3e^{2x}+2e^{2x}x-2sin(2x)
What is the first derivative of e^{2x}+xe^{2x}+cos(2x) ?
The first derivative of e^{2x}+xe^{2x}+cos(2x) is 3e^{2x}+2e^{2x}x-2sin(2x)