find dy.\ny = sin (7x²)\ndy = □ dx
find dy.\ny = sin (7x²)\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)). Let (u = 7x^{2}), so (y=\sin(u)). The derivative of (\sin(u)) with respect to (u) is (\cos(u)), and the derivative of (u = 7x^{2}) with respect to (x) is (u^\prime=14x).
Step2: Substitute back
Substitute (u = 7x^{2}) into the derivative. We get (y^\prime=\cos(7x^{2})\cdot14x).
Answer:
(14x\cos(7x^{2}))