Find the derivative of this function?

Question

#y=x(x^2-3)#

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Answer 1 · 2017-01-10T05:23:45

#dy/dx=3(x^2-1)#

Since this is problem in the Product Rule section we will apply it here;

The Product Rule states that:

If #y=f(x)*g(x)#
Then #dy/dx = f(x)*g'(x) + f'(x)*g(x)#

In our example:

#f(x) = x# and #g(x) = (x^2-3)#

Hence: #dy/dx= x*2x + 1*(x^2-3)#

#= 2x^2+x^2-3#

#=3(x^2-1)#

Note however that this problem is more simply solved by first expanding the expression and applying the Power Rule as follows:

#y=x(x^2-3)#

#= x^3-3x#

#dy/dx= 3x^2-3#

#=3(x^2-1)#