Implicit differentiation
take the deritivive with respect to x
first
y+2=(1/2)(x^2)-2sin(y)
take deritivitive
dy/dx+0=1/2(2x)-2(cosy)dy/dx
dy/dx=x-2cosy(dy/dx)
add 2cosy(dy/dx) to both sides
dy/dx+2cosy(dy/dx) =x
undistribute dy/dx
dy/dx(1+2cos(y))=x
divide both sides by 1+2cos(y)
![\frac{dy}{dx}= \frac{x}{1+2cos(y)}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D%20%5Cfrac%7Bx%7D%7B1%2B2cos%28y%29%7D%20%20)
at (2,0)
x=2
y=0
![\frac{dy}{dx}= \frac{2}{1+2cos(0)}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D%20%5Cfrac%7B2%7D%7B1%2B2cos%280%29%7D%20%20)
![\frac{dy}{dx}= \frac{2}{1+2(1)}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D%20%5Cfrac%7B2%7D%7B1%2B2%281%29%7D%20%20)
![\frac{dy}{dx}= \frac{2}{1+2}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D%20%5Cfrac%7B2%7D%7B1%2B2%7D%20%20)
![\frac{dy}{dx}= \frac{2}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D%20%5Cfrac%7B2%7D%7B3%7D%20%20)
the slope is 2/3
Answer:
the answer is 1 & 32/99 (131/99)
Substitute -8 in for a and 2 for b. Multiply -8 and 2 = -16. -16 / 4 = -4
Step-by-step explanation:
are you sure it is top? or what?
Answer:
Step-by-step explanation:
step 1 simplified like terms -11k +3k =8k
step 2 incorrect should be -4k -20 on the left side distributive property
step 3 added 8k to each side
step 4 added 20 to each side
step 5 divided each side by 4