/ 3 2\ log\2*x + 3*x /
d / / 3 2\\ --\log\2*x + 3*x // dx
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 6*x + 6*x ----------- 3 2 2*x + 3*x
/ 2\ | 6*(1 + x) | 6*|1 + 2*x - ----------| \ 3 + 2*x / ------------------------ 2 x *(3 + 2*x)
/ 3 \ | 36*(1 + x) 9*(1 + x)*(1 + 2*x)| 12*|1 + ------------ - -------------------| | 2 x*(3 + 2*x) | \ x*(3 + 2*x) / ------------------------------------------- 2 x *(3 + 2*x)