/ 3 2\ log\10*x - x /
log(10*x^3 - x^2)
Let .
The derivative of is .
Then, apply the chain rule. Multiply by :
Differentiate term by term:
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:
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:
The result is:
The result of the chain rule is:
Now simplify:
The answer is:
2 -2*x + 30*x ------------ 3 2 10*x - x
/ 2\ | 2*(-1 + 15*x) | 2*|-1 + 30*x - --------------| \ -1 + 10*x / ------------------------------ 2 x *(-1 + 10*x)
/ 3 \ | 4*(-1 + 15*x) 3*(-1 + 15*x)*(-1 + 30*x)| 4*|15 + -------------- - -------------------------| | 2 x*(-1 + 10*x) | \ x*(-1 + 10*x) / --------------------------------------------------- 2 x *(-1 + 10*x)
/ 3 \ | 4*(-1 + 15*x) 3*(-1 + 15*x)*(-1 + 30*x)| 4*|15 + -------------- - -------------------------| | 2 x*(-1 + 10*x) | \ x*(-1 + 10*x) / --------------------------------------------------- 2 x *(-1 + 10*x)