How can I find the derivative of #y=(x^2+1)^5#?

1 Answer
1s2s2p
Apr 20, 2018

#dy/dx=10x(x^2+1)^4#

Explanation:

If we write this as:
#y=u^5# then we can use the chain rule:
#dy/dx=(dy)/(du)*(du)/(dx)#

#(dy)/(du)=5u^4#

#(du)/(dx)=2x#

#dy/dx=(dy)/(du)*(du)/(dx)=10xu^4#

Putting back in #x^2+1# gives us:
#dy/dx=10x(x^2+1)^4#

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