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

The derivative of sin(xsin(x)) is sin(2x)

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

The first derivative of sin(xsin(x)) is sin(2x)

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

sin (2 x)

Solution steps

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

Simplify

sin (x) sin (x) : sin^{2} (x)

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

Apply the chain rule:

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

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

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

= 2 sin (x) cos (x)

Use the Double Angle identity:

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

= sin (2 x)

\frac{d}{d x} (x^{3} - 2 x + 7)

\frac{d}{d x} (cos (ln (x)) - sin (ln (x)))

\frac{d}{d y} (2 y^{3} + \frac{1}{24 y})

\frac{d}{d x} (3 x^{2} + 5 x)

x \to 1 + lim (x^{\frac{6}{1 - x}})

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