en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

derivative of

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

Solution

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}

Graph

Popular Examples

slope of y=3x^2-x+1 slope

y = 3 x^{2} - x + 1

x(dy}{dx}+3(y+x^2)=\frac{sin(x))/x

x \frac{d y}{d x} + 3 (y + x^{2}) = \frac{sin ( x )}{x}

integral of ysqrt(1+y^2)

\int y 1 + y^{2} d y

x^{''}-5x^'+6x=(t^2+t)sin(t)

x^{^{''}} - 5 x^{^{'}} + 6 x = (t^{2} + t) sin (t)

limit as x approaches-1-of g(x)

x \to - 1 - lim (g (x))

Frequently Asked Questions (FAQ)

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}