What is the derivative of sin^2(x-1) ?

The derivative of sin^2(x-1) is sin(2(-1+x))

What is the first derivative of sin^2(x-1) ?

The first derivative of sin^2(x-1) is sin(2(-1+x))

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\frac{d}{d x} (sin^{2} (x - 1))

sin (2 (- 1 + x))

Solution steps

\frac{d}{d x} (sin^{2} (x - 1))

Apply the chain rule:

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

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

\frac{d}{d x} (sin (x - 1)) = cos (x - 1)

= 2 sin (x - 1) cos (x - 1)

Use the Double Angle identity:

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

= sin (2 (- 1 + x))

What is the derivative of sin^2(x-1) ?
The derivative of sin^2(x-1) is sin(2(-1+x))
What is the first derivative of sin^2(x-1) ?
The first derivative of sin^2(x-1) is sin(2(-1+x))