How do you find the derivative of (1)/((1-x^2)^(1/2))?

1 Answer

Derivative of color(blue)(d/dx(1/(1-x^2)^(1/2))=x/(1-x^2)^(3/2))

Explanation:

Start with the given 1/(1-x^2)^(1/2)

d/dx(1/(1-x^2)^(1/2))=d/dx(1-x^2)^(-1/2)

d/dx(1/(1-x^2)^(1/2))=(-1/2)(1-x^2)^(-1/2-1)*d/dx(1-x^2)

d/dx(1/(1-x^2)^(1/2))=(-1/2)(1-x^2)^(-3/2)*(0-2x)

d/dx(1/(1-x^2)^(1/2))=(-1/2)(1-x^2)^(-3/2)*(-2x)

d/dx(1/(1-x^2)^(1/2))=x/(1-x^2)^(3/2)

God bless....I hope the explanation is useful.