What is the derivative of ysin(2x) ?

The derivative of ysin(2x) is (dy)/(dx)sin(2x)+cos(2x)*2y

What is the first derivative of ysin(2x) ?

The first derivative of ysin(2x) is (dy)/(dx)sin(2x)+cos(2x)*2y

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

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

Solution steps

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

Apply the Product Rule:

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

f = y, g = sin (2 x)

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

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

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

What is the derivative of ysin(2x) ?
The derivative of ysin(2x) is (dy)/(dx)sin(2x)+cos(2x)*2y
What is the first derivative of ysin(2x) ?
The first derivative of ysin(2x) is (dy)/(dx)sin(2x)+cos(2x)*2y