SOLUTION: Will someone please show me how to Find the derivative of: ln sin^(-1)x^(3), where sin is an inverse function of sin x. I would really appreciate a solution with steps. Thanks,

Algebra ->  Equations -> SOLUTION: Will someone please show me how to Find the derivative of: ln sin^(-1)x^(3), where sin is an inverse function of sin x. I would really appreciate a solution with steps. Thanks,       Log On


   

Question 335843: Will someone please show me how to Find the derivative of:
ln sin^(-1)x^(3), where sin is an inverse function of sin x.
I would really appreciate a solution with steps.
Thanks,
-Nick.
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
Is that ln%28arcsin%28x%29%2Ax%5E3%29?. This is why it is important to use proper grouping symbols. Perhaps you mean ln%28arcsin%28x%29%29%2Ax%5E3?
Anyway, using the former:
If so, we use the chain rule and product rule.
The derivative of the inside times the derivative of the outside.
Derivative of inside using product rule: 3x%5E2%2Aarcsin%28x%29%2Bx%5E3%2Fsqrt%281-x%5E2%29
Because the derivative of ln(x)=1/x, the derivative of the outside is: 1%2F%28arcsin%28x%29%2Ax%5E3%29
Multiply them: %283sqrt%281-x%5E2%29%2Aarcsin%28x%29%2Bx%29%2F%28x%2Asqrt%281-x%5E2%29%2Aarcsin%28x%29%29