What is the derivative of #1/(1 + x^4)^(1/2)#?

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Answer 1 · 2015-04-30T14:52:54

#(-2x^3)/(1+x^4)^(3/2)#

Solution:

rewrite: #1/(1 + x^4)^(1/2) = (1+x^4)^(-1/2)#

Now use the power rule and the chain rule (a combination sometimes called the generalized power rule)

The derivative is:

#-1/2 (1+x^4)^(-3/2) (4x^3) = (-2x^3)/(1+x^4)^(3/2)#

Answer 2 · 2015-04-30T14:54:52

The answer is:

This function can be written in this way:

#y=(1+x^4)^(-1/2)rArr#

#y'=-1/2(1+x^4)^(-1/2-1)*4x^3=-(2x^3)/sqrt((1+x^4)^3)#.