Homework SourseDifferentiate fx 2sinx2cosx2 Differentiate fx 2sinx2cosx2S
Differentiate f(x) = 2sin(x^2)*cos(x^2).
Differentiate f(x) = 2sin(x^2)*cos(x^2).
Solution
The function f(x) = 2sin(x^2)*cos(x^2) has to be differentiated. We use the product rule and the chain rule.
f\'(x) = 2sin(x^2)\'*cos(x^2) + 2sin(x^2)*cos(x^2)\'
=> f\'(x) = 2 cos (x^2)*2x*cos(x^2) - 2sin(x^2)*sin (x^2)*2x
=> f\'(x) = 4x (cos (x^2))^2 - 4x (sin (x^2))^2
=> f\'(x) = 4x (cos 2(x^2))
The derivative of f(x) = 2sin(x^2)*cos(x^2) is 4x*(cos 2(x^2))
