Question

Calculate dy/dx

y=3x-5/2x+4<----- use the quotient rule

Answer 1

do you know the rule?

Answer 2

Remember this...(low-d-hi minus hi-d-low)/low^2

Answer 3

So first things first...let's find the derivatives of the numerator and denominator, respectively. \[y = \frac{ high }{ low }\]
\[\frac{ d }{ dx }(3x-5) = 3\] \[\frac{d}{dx}(2x+4) = 2\]
Now, let's substitute them into the equation: \[\frac{low \frac{d }{ dx }high - high \frac{ d }{ dx } low}{ low ^{2} }\]
1. \[\frac{(2x+4) \frac{d }{ dx }(3x-5) - (3x-5) \frac{ d }{ dx } 2x+4}{ (2x+4)^{2} }\]
2. \[\frac{(2x+4)3 - (3x-5)2}{ (2x+4)^{2} }\]
3. Evaluate \[\frac{(6x+12) - (6x-10)}{ (2x+4)^{2} }\]
4. Foil the denominator (optional) \[\frac{2}{4x^{2}+16x+16}\]
Voilá!