How do you find the derivative of # (arcsinx)^7#?

1 Answer
mason m
Nov 30, 2016

#(7(arcsinx)^6)/sqrt(1-x^2)#

Explanation:

We know from the power rule that the derivative of #x^7# is #7x^6#. The chain rule tells us that when we have a function inside this, the derivative will be in the same form of #7("function")^6# but multiplied by the derivative of the inner function as well.

So, the derivative of #(f(x))^7# is #7(f(x))^6*f'(x)#. So, for this, we see that the derivative of #(arcsinx)^7# is #7(arcsinx)^6*1/sqrt(1-x^2)#, since the derivative of #arcsinx# is #1/sqrt(1-x^2)#.

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