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

1 Answer

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.