How do you differentiate #f(x)=1/(16x+3)^2# using the quotient rule?
2 Answers
Explanation:
#"given " f(x)=(g(x))/(h(x))" then"#
#f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larr" quotient rule"#
#g(x)=1rArrg'(x)=0#
#h(x)=(16x+3)^2#
#rArrh'(x)=2(16x+3).16=32(16x+3)larr" chain rule"#
#rArrf'(x)=((16x+3)^2 .0-32(16x+3))/(16x+3)^4#
#color(white)(rArrf'(x))=-32/(16x+3)^3#
Explanation:
We first find the derivative using the quotient rule:
Where
But we have
Now we clean it up:
We can cancel out just one
We now have:
Final answer: