Possible derivation:
d/dw(log(w)+(log(2, w))/(tan(w)))
Rewrite the expression: log(w)+(log(2, w))/(tan(w)) = log(w)+(cot(w) log(w))/(log(2)):
= d/dw(log(w)+(cot(w) log(w))/(log(2)))
Differentiate the sum term by term and factor out constants:
= d/dw(log(w))+(d/dw(cot(w) log(w)))/(log(2))
The derivative of log(w) is 1/w:
= (d/dw(cot(w) log(w)))/(log(2))+1/w
Use the product rule, d/dw(u v) = v ( du)/( dw)+u ( dv)/( dw), where u = cot(w) and v = log(w):
= 1/w+log(w) (d/dw(cot(w)))+cot(w) (d/dw(log(w)))/(log(2))
The derivative of cot(w) is -csc^2(w):
= 1/w+(cot(w) (d/dw(log(w)))+-csc^2(w) log(w))/(log(2))
The derivative of log(w) is 1/w:
= 1/w+(-(csc^2(w) log(w))+1/w cot(w))/(log(2))
Simplify the expression:
Answer: | = 1/w+((cot(w))/w-csc^2(w) log(w))/(log(2))
