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

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Answer 1 · 2016-02-24T23:49:42

$dy/dx=(5x^4)/sqrt(1-x^10)$

Use the chain rule . To do this, you must first know that

$d/dxarcsin(x)=1/sqrt(1-x^2)$

Thus,

$d/dxarcsin(f(x))=1/sqrt(1-(f(x))^2)*f'(x)$

So, for $arcsin(x^5)$ we see that $f(x)=x^5$ , and

$dy/dx=d/dxarcsin(x^5)=1/sqrt(1-(x^5)^2)*d/dx(x^5)$

$dy/dx=(5x^4)/sqrt(1-x^10)$

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