<u>Differentiate using the Quotient Rule</u> –
![\pink{\twoheadrightarrow \sf \dfrac{d}{dx} \bigg[\dfrac{f(x)}{g(x)} \bigg]= \dfrac{ g(x)\:\dfrac{d}{dx}\bigg[f(x)\bigg] -f(x)\dfrac{d}{dx}\:\bigg[g(x)\bigg]}{g(x)^2}}\\](https://tex.z-dn.net/?f=%5Cpink%7B%5Ctwoheadrightarrow%20%5Csf%20%5Cdfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%5Cdfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%20%5Cbigg%5D%3D%20%5Cdfrac%7B%20g%28x%29%5C%3A%5Cdfrac%7Bd%7D%7Bdx%7D%5Cbigg%5Bf%28x%29%5Cbigg%5D%20-f%28x%29%5Cdfrac%7Bd%7D%7Bdx%7D%5C%3A%5Cbigg%5Bg%28x%29%5Cbigg%5D%7D%7Bg%28x%29%5E2%7D%7D%5C%5C)
According to the given question, we have –
- f(x) = x^3+5x+2
- g(x) = x^2-1
Let's solve it!
![\green{\twoheadrightarrow \bf \dfrac{d}{dx}\bigg[ \dfrac{x^3+5x+2 }{x^2-1}\bigg]} \\](https://tex.z-dn.net/?f=%5Cgreen%7B%5Ctwoheadrightarrow%20%5Cbf%20%5Cdfrac%7Bd%7D%7Bdx%7D%5Cbigg%5B%20%5Cdfrac%7Bx%5E3%2B5x%2B2%20%7D%7Bx%5E2-1%7D%5Cbigg%5D%7D%20%5C%5C)
An equation for the ellipse ( standard form ):
x²/a² + y²/b² = 1
Here is: a - semi-major axis and b - semi-minor axis.
Radius of the moon is 1,000 km and the distance from the surface of the moon to the satellite varies from 953 km to 466 km.
a = 1,000 + 953 = 1,953 km
b = 1,000 + 466 = 1,466 km
Answer:
The equation is x² / 1,953² + y² / 1,466² = 1
or: x²/3,814,209 + y²/2,149,156 = 1
We will say that the eastbound cyclist is going x mph. This means that the westbound cyclist is going x+3 mph.
They are both cycling for 6 hours and end up 162 miles apart.
Distance=rate*time
6x+6(x+3)=162
6x+6x+18+162
12x=144
x=12
So, the eastbound cyclist is going 12 mph.
Remember the westbound cyclist is going 3 mph faster, so s/he is going 15 mph.
Hope this helps!!
The first one would be 190 and the second one would be 107
1/12 + 5/12 + 1/4 + 1/4 = 6/12 + 2/4 = 6/12 + 6/12 = 12/12 = 1
Yes, they did.
