Find f ′ (x) for f (x) = sin (3x2).

Assuming you mean f (x) = sin (3x²)

Use chain rule to differentiate as we can view this as a composite function.

The outside "function" is sin (x); the inside "function" is 3x^2

The derivative of the composite function we get by

⇒ Differentiating the outside function: so we have cos (x). Then stick the inside function into that.

⇒ After that, multiply by the derivative of the inside function. The derivative of the inside function is 6x.

f (x) = sin (3x²)

f' (x) = cos (3x²) · (3x²) '

f' (x) = cos (3x²) · 6x

f' (x) = 6x cos (3x²)

The answer is f' (x) = 6x cos (3x²)