How do you find the derivative of the function: #y = arcsin(5x)#?

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Answer 1 · 2018-03-07T13:13:58

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

Just a simple application of the chain rule which states that
#d/dx f(g(x)) = f'(g(x))*g'(x)#

where #f(x) = arcsin(x)#
and #g(x) = 5x#

recall that the derivative of #arcsin(x)# is # 1/(1-x^2)# and of #5x# is #5#

therefore,

the entire derivative is
#1/(1-(5x)^2) * 5#
=
which is equal to

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