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

1 Answer
Mar 12, 2017

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

Explanation:

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)#