Question

Derivar la siguiente funcion
f(x)=7x^2-x+e^2
___________
Sen (x-3)

Answer 1

$f(x)= \frac{7x\²-x+e\²}{sen(x-3)} \\ \\ f'(x)= \frac{(7x\²-x+e\²)'(sen(x-3)-(7x\²-x+e\²)(sen(x-3)'}{[sen(x-3)]\²} \\ \\f'(x)= \frac{(14x-1)(sen(x-3)-(7x\² -x+e\²)(cos(x-3)}{sen\²(x-3)} \\ \\ f'(x)=(14x-1)cosec(x-3)-(7x\²-x+e\²)tang(x-3)cosec(x-3) \\ \\ \boxed{\boxed{f'(x)=cosec(x-3)[14x-1-(7x\²-x+e\²)tang(x-3)]}}\\ \\ .$