5 / 2 \ \x - 3*x/
/ 5\ d |/ 2 \ | --\\x - 3*x/ / dx
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
Apply the power rule: goes to
The derivative of a constant times a function is the constant times the derivative of the function.
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
So, the result is:
The result is:
The result of the chain rule is:
Now simplify:
The answer is:
4 / 2 \ \x - 3*x/ *(-15 + 10*x)
3 3 / 2 \ 10*x *(-3 + x) *\2*(-3 + 2*x) + x*(-3 + x)/
2 2 / 2 \ 60*x *(-3 + x) *(-3 + 2*x)*\(-3 + 2*x) + 2*x*(-3 + x)/