How do you find the derivative of the function: #tan(arcsin x)#?

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Answer 1 · 2016-01-08T08:09:46

#Sec^2(arcsin x)/sqrt(1-x^2)#

or #Sec^2(sin^-1 x)/sqrt(1-x^2)#

to find the derivative of the function #tan(arcsin x)#, use the following formulas for differentiation

#d/dx(tan u) = sec^2 u * d/dx(u)# and

#d/dx(arcsin u)= 1/sqrt(1-u^2)*d/dx(u)#

let me continue

from the given #tan(arcsin x)#

#d/dx(tan(arcsin x))=sec^2 (arcsin x)*d/dx(arcsin x)#

#= sec^2 (arcsin x)*(1/sqrt(1-x^2))*d/dx(x)#

the final answer is

#= sec^2 (arcsin x)/sqrt(1-x^2)#