Answer:
Given: y = 7x^9sin(x)cos(x)
Using the product rule, we differentiate each term separately:
dy/dx = (d/dx)[7x^9sin(x)cos(x)]
= 7[(d/dx)(x^9sin(x)cos(x))] + 7x^9[(d/dx)(sin(x)cos(x))]
Now, let's differentiate each term further using the chain rule:
(dy/dx) = 7[(d/dx)(x^9sin(x)cos(x))] + 7x^9[(d/dx)(sin(x)cos(x))]
= 7[(9x^8sin(x)cos(x)) + (x^9cos^2(x) - x^9sin^2(x))]
= 63x^8sin(x)cos(x) + 7x^9(cos^2(x) - sin^2(x))
Therefore, dy/dx = 63x^8sin(x)cos(x) + 7x^9(cos^2(x) - sin^2(x)).
Explanation: