Question

Differentiate the following: f(x)=(ax+b)/(cx+d)

Answer 1

Use product rule to differentiate it: \[\large \frac{d}{dx}(\frac{f(x)}{g(x)})=\frac{f'(x)g(x)-f(x)g'(x)}{(g(x))^2}\]

Answer 2

right zepp - except thats the quotient rule

Answer 3

oright >_>

Answer 4

So in this case, \[\large \frac{d}{dx}(\frac{ax+b}{cx+d})=\frac{(\frac{d}{dx}(ax+b))(cx+d)-(ax+b)(\frac{d}{dx}(cx+d))}{(cx+d)^2}\]

Answer 5

I did that and got
[(ax+1)(cx+d)-(cx+1)(ax+b)]/(cx+d)^2
but this is not right

Answer 6

That's because you did it wrong
Okay let's go steps by steps, let f(x) be ax+b, can you find f'(x)?

Answer 7

is that (ax+1)?

Answer 8

Nope, remember \(\large \frac{d}{dx}cx=c\) where c is a constant

Answer 9

so its 0

Answer 10

In this case, it could be written as \[\large \frac{d}{dx}(ax+1)=\frac{d}{dx}(ax)+\frac{d}{dx}(1)\]

Answer 11

\[\large \frac{d}{dx}(ax+b)=\frac{d}{dx}(ax)+\frac{d}{dx}(b)\] sorry

Answer 12

Derivative of ax is a, derivative of b is 0, since it's a constant.

Answer 13

Therefore, the derivative of ax+b = a

Answer 14

Let \[\large f(x)=ax+b; f'(x)=a\\\large g(x)=cx+d; g'(x)=c\]

Answer 15

\[\large \frac{d}{dx}(\frac{ax+b}{cx+d})=\frac{(\frac{d}{dx}(ax+b))(cx+d)-(ax+b)(\frac{d}{dx}(cx+d))}{(cx+d)^2}\\ \large =\frac{a(cx+d)-c(ax+b)}{(cx+d)^2}\]

Answer 16

Thanks that makes sense now. I see what i was doing wrong

Answer 17

Alright :)