How do you differentiate #y= -cos^-1 (1/x^5)#? Calculus Basic Differentiation Rules Chain Rule 1 Answer Bdub May 6, 2016 #y'=-5/(x^6(sqrt(1-1/x^10))# Explanation: Use chain rule #f(g(x))'=f'(g(x))*g'(x)#and derivative property#cos^-1 x=-1/sqrt(1-x^2)# #y'=-[-1/sqrt(1-(1/x^5)^2) *(-5)/x^6]# #y'=-5/(x^6(sqrt(1-1/x^10))# Answer link Related questions What is the Chain Rule for derivatives? How do you find the derivative of #y= 6cos(x^2)# ? How do you find the derivative of #y=6 cos(x^3+3)# ? How do you find the derivative of #y=e^(x^2)# ? How do you find the derivative of #y=ln(sin(x))# ? How do you find the derivative of #y=ln(e^x+3)# ? How do you find the derivative of #y=tan(5x)# ? How do you find the derivative of #y= (4x-x^2)^10# ? How do you find the derivative of #y= (x^2+3x+5)^(1/4)# ? How do you find the derivative of #y= ((1+x)/(1-x))^3# ? See all questions in Chain Rule Impact of this question 1089 views around the world You can reuse this answer Creative Commons License