Find the derivative of this function?

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

Answer 1

Charles Arocha

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

We will apply it here since it is a problem in the Product Rule section;

According to the Product Rule:

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

In our illustration:

#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)#

However, keep in mind that solving this issue more easily requires first expanding the expression and then using the Power Rule as follows:

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

#= x^3-3x#

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

#=3(x^2-1)#

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Answer 2

Elijah Abram

To assist you accurately, I need the specific function for which you want to find the derivative. Could you please provide the function?

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.