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

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

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

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

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derivative of

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)

\int cos (x) sin^{2} (x) d x

x \to 1 lim (1 + x)

\int \frac{x \cdot ( arctan ( x ) )}{( 1 + x ^{2} ) ^{2}} d x

t^{4} - 8 t

- 9

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