find dy.\ny = sin(15x²)\ndy = □ dx
find dy.\ny = sin(15x²)\ndy = □ dx
Answer
Explanation:
Step1: Apply the chain rule
The chain rule states that if (y = f(g(x))), then (y^\prime=f^\prime(g(x))\cdot g^\prime(x)). Here (y = \sin(u)) with (u = 15x^{2}). The derivative of (\sin(u)) with respect to (u) is (\cos(u)), and the derivative of (u = 15x^{2}) with respect to (x) is (u^\prime=30x).
Step2: Substitute back (u = 15x^{2})
By the chain rule, (\frac{dy}{dx}=\cos(15x^{2})\cdot30x). Then, since (dy=\frac{dy}{dx}dx), we have (dy = 30x\cos(15x^{2})dx).
Answer:
(30x\cos(15x^{2}))