CALCULUS O.O DUE AT 11?
im almost done but these im stuck on...
4.If 6x = e^(10y) then find dy/dx when x =1/6. Hint: your derivative will have y in it, so you will need to determine the value of y that corresponds with x =1/6
7.find the slope of the normal line to the curve 5x^2-10y^2=5xy at the point (1,-1)
8.if 6f(x)=xsin(f(x))=5x^3 and f(sqrt(3)/2)=Pi/6 then find f ' (sqrt(3)/2)
Answers & Comments
Find y when x = 1/6:
6(1/6) = e^(10y)
1 = e^(10y)
10y = 0
y = 0
Find dy/dx:
d/dx(6x) = d/dx(e^(10y))
6 = e^(10y)10dy/dx
dy/dx = 6/(10e^(10y)) = 3/(5e^(10y)
dy/dx(y = 0) = 3/(5e^(10(0))) = 3/5
One question at a time.
4.
6x = e^10y
ln(6x) = ln(e^10y)
ln(6x) = 10y*ln(e)
ln(6x) = 10y*1
y = ln(6x)/10
now we know that the function is y = ln(6x)/10,so
y' = ((6/x)10- (0)(ln(x))/100
y' = (60/x)/100
y'(1/6)=(10)/100
y'= 1/10