What is the derivative of this function #sin^-1 (5x)#?

2 Answers
Apr 13, 2017

#(sin^(-1)(5x))'=5/sqrt(1-25x^2)#

Explanation:

Recall:

#(sin^(-1)u)'=1/sqrt(1-u^2)#

By the above rule (#u=5x#) along with Chain Rule,

#(sin^(-1)(5x))'=1/sqrt(1-(5x)^2)cdot(5x)' =5/sqrt(1-25x^2)#

I hope that this was clear.

Apr 13, 2017

#5/(sqrt(1-25x^2))#

Explanation:

#color(orange)"Reminder " d/dx(sin^-1x)=1/(sqrt(1-x^2))#

#"and " d/dx(sin^-1(f(x)))=(f'(x))/(sqrt(1-f(x)^2)#

#rArrd/dx(sin^-1(5x))#

#=5/(sqrt(1-(5x)^2))#

#=5/(sqrt(1-25x^2))#