Question

Find the derivative of the function

Answer 1

Hello from MrBillDoesMath!

Answer:

27 x^2 sqrt(x^3) sin(x^3) - 9/2 sqrt(x^1/2) sin(x^1/2)*x^(-1/2)

Discussion:

Let f(t) - 9 sqrt(t) sin(t), then

y' = f(x^3) * d(x^3)/dx  - f(sqrt(x)) * d(x^1/2)/dx

   = (9 sqrt(x^3)sin(x^3)) * 3x^2 -  (9 sqrt(x^1/2)sin(x^1/2)) * (1/2) x^-(1/2)

   = 27 x^2 sqrt(x^3) sin(x^3) - 9/2 sqrt(x^1/2) sin(x^1/2)*x^(-1/2)

Hope I didn't make a "bozo" error differentiating things!

Thank you,

MrB