How do you find the derivative of y =sqrt(1-x^2)?
3 Answers
Jul 29, 2014
y'=-x/(sqrt(1-x^2)) Using Chain Rule
y=sqrt(f(x))
y'=1/(2sqrt(f(x)))*f'(x) Similarly, following for the above function,
y'=(sqrt(1-x^2))'
y'=1/(2sqrt(1-x^2))*(1-x^2)'
y'=1/(2sqrt(1-x^2))*(-2x)
y'=-x/(sqrt(1-x^2))
Jun 3, 2017
Explanation:
Another method is using implicit differentiation like this:
y = sqrt(1-x^2)
y^2 = 1 - x^2
x^2 + y^2 = 1
Now differentiate with respect to
2x + 2y(dy/dx) = 0
x + y(dy/dx) = 0
y(dy/dx) = -x
(dy/dx) = -x/y
Finally, make the substitution
dy/dx = -x/(sqrt(1-x^2))
Final Answer
Jun 3, 2017
Explanation:
Now let
Now apply the chain rule: