What is the derivative of sin x^-1 ?

1 Answer
Mar 12, 2018

= -cscx*cotx=cscxcotx

Explanation:

Let f(x)= sinx^(-1)f(x)=sinx1
Using chain rule and the power rule,
thereby differentiating the given function,

The chain rule:

d/dx(g(h(x)))=g'(h(x))*h'(x)

The power rule:

d/dx(x^n)=nx^(n-1) when n is a constant.

d/dx(sinx)=cosx

f'(x)= d/(dx)[(sinx)^(-1)]

= (-1)(sinx)^(-2)*d/(dx)[(sinx)]

= -1/((sinx)^2) * cosx

= -1/(sinx)*1/sinx*cosx

= -1/(sinx)*cosx/sinx

= -cscx*cotx