Differentiate with regard to x: y=cos^-1(x/a)+(a^2-x^2)^1/2

Question

Differentiate w.r.t x

Answer 1

y = cos^-1(x/a) + √(a² - x²)

 

 

y' = [-1/√(1 - (x/a)²)](1/a) + [1/(2√(a² - x²))](-2x)

 

= -1/√(a² - x²) - x/√(a² - x²)

 

= (-x - 1)/√(a² - x²)