while differentiating variable y you have to write dy/dx
as in question 1 (2/3)x^(-1/3) + (2/3)y^(-1/3)dy/dx = 0
I am having difficulty differentiating the following questions
1. x^(2/3)+y(2/3)=5 This is what I did
(2/3)x^(-1/3)+(2/3)y^(-1/3) I am also supposed to plot the point(8,1) to find slope
2. tan(x+y)=x This is what I did
sec^2(x+y)(1+1)=1 ? (is this correct?)
3. y=sin(xy)
1=cos(xy)(1y+1x) is this correct?
From here, plug in x = 8 and y = 1 to solve for (dy/dx).
For 3. NO.
The derivative of y is NOT ONE!!
The derivative of y is
dy/dx, or y'.
You should have y' = cos(xy)*(xy)' -->
y' = cos(xy)*(xy' + yx'), but x' IS ONE, so we can write this as
y' = cos(xy)*(xy' + y), or
dy/dx = cos(xy)*(x*dy/dx + y)