What is the derivative of f(x)=sin(2x)cos(2x) ?

The derivative of f(x)=sin(2x)cos(2x) is 2cos(4x)

What is the first derivative of f(x)=sin(2x)cos(2x) ?

The first derivative of f(x)=sin(2x)cos(2x) is 2cos(4x)

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derivative of

f (x) = sin (2 x) cos (2 x)

2 cos (4 x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= cos (2 x) \cdot 2 cos (2 x) + (- sin (2 x) \cdot 2) sin (2 x)

Simplify

cos (2 x) \cdot 2 cos (2 x) + (- sin (2 x) \cdot 2) sin (2 x) : 2 cos (4 x)

= 2 cos (4 x)

\frac{4 x}{x + 1}

\int e^{- 5 x} sin (4 x) d x

\frac{d y}{d x} = \frac{x}{y}, y (0) = - 4

x^{2} y^{^{''}} - 3 x y^{^{'}} + 4 y = 0

ln (x), x = 4

What is the derivative of f(x)=sin(2x)cos(2x) ?
The derivative of f(x)=sin(2x)cos(2x) is 2cos(4x)
What is the first derivative of f(x)=sin(2x)cos(2x) ?
The first derivative of f(x)=sin(2x)cos(2x) is 2cos(4x)