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OpenStudy (anonymous):
Let f(x)=7sin^-1(x^4) Find f'(x)
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OpenStudy (anonymous):
ok. let's take it one at a time. what's the derivative of arcsinx?
OpenStudy (anonymous):
1/(sqrt1-x^2)
OpenStudy (anonymous):
yep, so plug in x^4 into your x
OpenStudy (anonymous):
and afterwards don't forget the chain rule. You'll have to multiply by the derivative of the inner function
OpenStudy (anonymous):
So 1/(sqrt1-(x^4)^2)?
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OpenStudy (anonymous):
multiplied by the inner function and don't forget the 7.
OpenStudy (anonymous):
\[\frac{ 28x ^{3} }{ \sqrt{1-x ^{8}} }\]
OpenStudy (anonymous):
I believe that is your answer.
OpenStudy (anonymous):
Thanks!
OpenStudy (anonymous):
basically just a mini summary, you would take the derivative of the outer function, which would be 7arcsin and plug in the x that they give you, multiplied by the derivative of the inner function which would be x^4
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