Question

if y^2=sin(x), determine dy/dx

Answer 1

y^2=sin(x)

derive both sides with respect to x to get

d/dx[y^2]=d/dx[sin(x)]

2y*y' = cos(x)

Then solve for y' to get

2y*y' = cos(x)

y' = cos(x)/2y

y' = cos(x)/(2*sqrt(sin(x)))

Finally, replace y' with dy/dx

dy/dx = cos(x)/(2*sqrt(sin(x)))

Answer 2

thank you

Answer 3

np