What is the derivative of 1/2 tan(xsin(2x)) ?

The derivative of 1/2 tan(xsin(2x)) is sin(2x)

What is the first derivative of 1/2 tan(xsin(2x)) ?

The first derivative of 1/2 tan(xsin(2x)) is sin(2x)

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\frac{d}{d x} (\frac{1}{2} tan (x) sin (2 x))

sin (2 x)

Solution steps

\frac{d}{d x} (\frac{1}{2} tan (x) sin (2 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2} \frac{d}{d x} (tan (x) sin (2 x))

Apply the Product Rule:

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

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

= \frac{1}{2} (\frac{d}{d x} (tan (x)) sin (2 x) + \frac{d}{d x} (sin (2 x)) tan (x))

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

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

= \frac{1}{2} (sec^{2} (x) sin (2 x) + cos (2 x) \cdot 2 tan (x))

Simplify

\frac{1}{2} (sec^{2} (x) sin (2 x) + cos (2 x) \cdot 2 tan (x)) : sin (2 x)

= sin (2 x)

\int 25 sec^{5} (x) d x

y^{^{''}} + 7 y^{^{'}} + 10 y = 14 x e^{3 x}

\frac{d u}{d v}, u + v = 5

\int (\frac{1}{3} e^{x + 3} + \frac{3}{x} - 5) d x

\int \frac{x ^{2} - 11 x - 18}{x ( x ^{2} + 3 x + 3 )} d x

What is the derivative of 1/2 tan(xsin(2x)) ?
The derivative of 1/2 tan(xsin(2x)) is sin(2x)
What is the first derivative of 1/2 tan(xsin(2x)) ?
The first derivative of 1/2 tan(xsin(2x)) is sin(2x)