How do you calculate the derivate for #f(x)=[(x+2)/(x+1)](2x-7)#?

1 Answer
Aug 1, 2015

Answer:

Using a combination of Product Rule and Quotient Rule.

Explanation:

Product Rule:
If #f(x)=g(x)\cdot h(x)#,
then #f^\prime(x)=g(x)\cdot h\prime (x)+h(x)\cdot g\prime (x)#

Quotient Rule:
If #f(x)=\frac{g(x)}{h(x)}#
then #f^\prime(x)=\frac{h(x)\cdot g\prime (x)-g(x)\cdot h\prime (x)}{h(x)^2}#

Now, you can express #f(x)# as

#f(x)=\underbrace{g(x)\cdot h(x)}_\text{product rule}#,

where #g(x)=\underbrace{\frac{x+2}{x+1}}_\text{quotient rule}# and #h(x)=2x-7#

OR as

#f(x)=\underbrace{\frac{g(x)}{h(x)}}_\text{quotient rule}#,

where #g(x)=\underbrace{(x+2)(2x-7)}_\text{product rule}# and #h(x)=x+1#.

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