How do you differentiate #g(x) =x^2sinx# using the product rule?

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How do you differentiate #g(x) =x^2sinx# using the product rule?

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Answer 1 · 2015-12-24T14:36:27

The trick is to find the two functions where product rule can be applied. Please go through the explanation for the step by step application of the product rule.

Explanation:

The product rule where #u# and #v# are functions of #x#

#(uv)' = u'v+v'u#

The given problem is #g(x) = x^2 sin(x)#

#g(x)=(uv)#
#u=x^2# and #v=sin(x)#

Now to find #u'# and #v'#

#u=x^2#
#u'=2x#

#v=sin(x)#
#v'=cos(x)#

#g'(x) =(uv)' = (2x)(sin(x)) + x^2cos(x)#

#g'(x) = 2xsin(x)+x^2cos(x)# Answer

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How do you differentiate #g(x) =x^2sinx# using the product rule?

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