What is the derivative of sin(x²+1)according to x?

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Answer 1 · 2017-03-12T03:22:35

#2x*cos(x^2 +1)#

Inside of our #sin(x)# function is another function "#x^2 +1#" so we have to use the chain rule.

The derivative of the inside function #x^2 +1# is #2x#
(#x^2# becomes #2x^(2-1)# according to the power rule, 1 becomes 0 as it is a constant)

Now applying the chain rule (leaving the inside function unchanged):

#2x*d/dx(sin(x))#

The derivative of #sin(x)# is #cos(x)#, so we find

#d/dx(sin(x^2+1))# =

#2x*cos(x^2+1)#