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

1 Answer
mason m
Feb 24, 2016

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

Explanation:

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)#

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