What is the derivative of y=e^{2x}tan(2x) ?

The derivative of y=e^{2x}tan(2x) is e^{2x}*2tan(2x)+sec^2(2x)*2e^{2x}

What is the first derivative of y=e^{2x}tan(2x) ?

The first derivative of y=e^{2x}tan(2x) is e^{2x}*2tan(2x)+sec^2(2x)*2e^{2x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

y = e^{2 x} tan (2 x)

e^{2 x} \cdot 2 tan (2 x) + sec^{2} (2 x) \cdot 2 e^{2 x}

Solution steps

\frac{d}{d x} (e^{2 x} tan (2 x))

Apply the Product Rule:

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

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

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

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

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

= e^{2 x} \cdot 2 tan (2 x) + sec^{2} (2 x) \cdot 2 e^{2 x}

What is the derivative of y=e^{2x}tan(2x) ?
The derivative of y=e^{2x}tan(2x) is e^{2x}*2tan(2x)+sec^2(2x)*2e^{2x}
What is the first derivative of y=e^{2x}tan(2x) ?
The first derivative of y=e^{2x}tan(2x) is e^{2x}*2tan(2x)+sec^2(2x)*2e^{2x}