For implicit differentiation, you are using the chain rule
![f'(x) = g'(u(x))* \frac{du}{dx}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20g%27%28u%28x%29%29%2A%20%5Cfrac%7Bdu%7D%7Bdx%7D)
Except u(x) = y, So after every "y" term is differentiated it will be multiplied by dy/dx.
17)
![y^3 +4 = 3x \\ 3y^2 \frac{dy}{dx} +0 = 3](https://tex.z-dn.net/?f=y%5E3%20%2B4%20%3D%203x%20%5C%5C%203y%5E2%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%2B0%20%3D%203)
Then you solve for dy/dx as if its a variable.
![\frac{dy}{dx} = \frac{3}{3y^2} = \frac{1}{y^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B3%7D%7B3y%5E2%7D%20%3D%20%5Cfrac%7B1%7D%7By%5E2%7D%20)
18) Here lets review product rule:
![(fg)' = f'g + fg'](https://tex.z-dn.net/?f=%28fg%29%27%20%3D%20f%27g%20%2B%20fg%27)
Take derivative of each term
![2x^2 = -3y^3 +3x^2y^3 \\ 4x = -9y^2 \frac{dy}{dx} + (6x)(y^3) + (3x^2)(3y^2 \frac{dy}{dx}) \\ 4x = -9y^2 \frac{dy}{dx} +6xy^3 +9x^2y^2 \frac{dy}{dx}](https://tex.z-dn.net/?f=2x%5E2%20%3D%20-3y%5E3%20%2B3x%5E2y%5E3%20%20%5C%5C%204x%20%3D%20-9y%5E2%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%2B%20%286x%29%28y%5E3%29%20%2B%20%283x%5E2%29%283y%5E2%20%5Cfrac%7Bdy%7D%7Bdx%7D%29%20%20%5C%5C%204x%20%3D%20-9y%5E2%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%2B6xy%5E3%20%2B9x%5E2y%5E2%20%5Cfrac%7Bdy%7D%7Bdx%7D)
Solve for dy/dx using factoring:
Answer:
Step-by-step explanation:
(a). SR = 15√2 km ≈ 21.2 km
R is 21.2 km due South-East of S
(b). RQ² = 35² + 15² ⇒ RQ = 5√14 km ≈ 38.1 km
R is 38.1 km due South-West of Q
Answer:
equation; P=A(1+r/n)^nt
P=principal amount
A=value of investment
r= interest rate in decimals
n=number of times compounded
t=time in years
P=1000(1+0.16/12)^12(5)= $2213.8 rounded
Step-by-step explanation:
Answer:
where is the graph
Step-by-step explanation: