What is the derivative of sin x^-1 ?

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Answer 1 · 2018-03-12T20:25:28

#= -cscx*cotx#

Let #f(x)= sinx^(-1)#
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#