# 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: