2 / x \ log (x)*sin\7 + 2/
log(x)^2*sin(7^x + 2)
Apply the product rule:
; to find :
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of is .
The result of the chain rule is:
; to find :
Let .
The derivative of sine is cosine:
Then, apply the chain rule. Multiply by :
Differentiate term by term:
The derivative of the constant is zero.
The result is:
The result of the chain rule is:
The result is:
Now simplify:
The answer is:
/ x \ 2*log(x)*sin\7 + 2/ x 2 / x \ -------------------- + 7 *log (x)*cos\7 + 2/*log(7) x
/ x\ x / x\ 2*(-1 + log(x))*sin\2 + 7 / x 2 2 / / x\ x / x\\ 4*7 *cos\2 + 7 /*log(7)*log(x) - --------------------------- - 7 *log (7)*log (x)*\- cos\2 + 7 / + 7 *sin\2 + 7 // + ------------------------------ 2 x x
/ x\ x 2 / / x\ x / x\\ x / x\ 2*(-3 + 2*log(x))*sin\2 + 7 / x 3 2 / / x\ 2*x / x\ x / x\\ 6*7 *log (7)*\- cos\2 + 7 / + 7 *sin\2 + 7 //*log(x) 6*7 *(-1 + log(x))*cos\2 + 7 /*log(7) ----------------------------- - 7 *log (7)*log (x)*\- cos\2 + 7 / + 7 *cos\2 + 7 / + 3*7 *sin\2 + 7 // - ---------------------------------------------------- - ------------------------------------- 3 x 2 x x