cos(x) -7 --------- log(x)
(-7^cos(x))/log(x)
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.
Let .
Then, apply the chain rule. Multiply by :
The derivative of cosine is negative sine:
The result of the chain rule is:
So, the result is:
To find :
The derivative of is .
Now plug in to the quotient rule:
Now simplify:
The answer is:
cos(x) cos(x) 7 7 *log(7)*sin(x) --------- + --------------------- 2 log(x) x*log (x)
/ 2 \ | 1 + ------ | cos(x) |/ 2 \ log(x) 2*log(7)*sin(x)| -7 *|\-cos(x) + sin (x)*log(7)/*log(7) + ---------- + ---------------| | 2 x*log(x) | \ x *log(x) / ---------------------------------------------------------------------------- log(x)
/ / 3 3 \ \ | 2*|1 + ------ + -------| / 2 \ | | | log(x) 2 | / 2 \ 3*|1 + ------|*log(7)*sin(x)| cos(x) | / 2 2 \ \ log (x)/ 3*\-cos(x) + sin (x)*log(7)/*log(7) \ log(x)/ | 7 *|- \1 - log (7)*sin (x) + 3*cos(x)*log(7)/*log(7)*sin(x) + ------------------------ + ----------------------------------- + ----------------------------| | 3 x*log(x) 2 | \ x *log(x) x *log(x) / ----------------------------------------------------------------------------------------------------------------------------------------------------------------- log(x)