What is the derivative of sin(xsin(2x)) ?

The derivative of sin(xsin(2x)) is cos(x)sin(2x)+cos(2x)*2sin(x)

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

The first derivative of sin(xsin(2x)) is cos(x)sin(2x)+cos(2x)*2sin(x)

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

What is the derivative of sin(xsin(2x)) ?
The derivative of sin(xsin(2x)) is cos(x)sin(2x)+cos(2x)*2sin(x)
What is the first derivative of sin(xsin(2x)) ?
The first derivative of sin(xsin(2x)) is cos(x)sin(2x)+cos(2x)*2sin(x)