log(x) 3*------*(4*x + 5) - 6*x log(2)
(3*(log(x)/log(2)))*(4*x + 5) - 6*x
Differentiate term by term:
Apply the quotient rule, which is:
and .
To find :
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the product rule:
; to find :
Differentiate term by term:
The derivative of the constant is zero.
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:
; to find :
The derivative of is .
The result is:
So, the result is:
To find :
The derivative of the constant is zero.
Now plug in to the quotient rule:
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:
Now simplify:
The answer is:
12*log(x) 3*(4*x + 5) -6 + --------- + ----------- log(2) x*log(2)
/ 5 + 4*x\ 3*|8 - -------| \ x / --------------- x*log(2)