What is the derivative of g(x)=tan(2x)*sin(2x) ?

The derivative of g(x)=tan(2x)*sin(2x) is 2sin(2x)+2sec(2x)tan(2x)

What is the first derivative of g(x)=tan(2x)*sin(2x) ?

The first derivative of g(x)=tan(2x)*sin(2x) is 2sin(2x)+2sec(2x)tan(2x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

g (x) = tan (2 x) \cdot sin (2 x)

2 sin (2 x) + 2 sec (2 x) tan (2 x)

Solution steps

\frac{d}{d x} (tan (2 x) sin (2 x))

Apply the Product Rule:

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

f = tan (2 x), g = sin (2 x)

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

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

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

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

Simplify

sec^{2} (2 x) \cdot 2 sin (2 x) + cos (2 x) \cdot 2 tan (2 x) : 2 sin (2 x) + 2 sec (2 x) tan (2 x)

= 2 sin (2 x) + 2 sec (2 x) tan (2 x)

d er i v a t i v e y = 2 x - x^{2}

\frac{d}{d θ} (2 + 2 sin (θ))

\int cos^{2} (π t) sin (π t) d t

\frac{d}{d x} (\frac{3 x}{x + 1})

d er i v a t i v e x^{2} e^{- 7 x}

What is the derivative of g(x)=tan(2x)*sin(2x) ?
The derivative of g(x)=tan(2x)*sin(2x) is 2sin(2x)+2sec(2x)tan(2x)
What is the first derivative of g(x)=tan(2x)*sin(2x) ?
The first derivative of g(x)=tan(2x)*sin(2x) is 2sin(2x)+2sec(2x)tan(2x)