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How do you find the derivative of #((1+3x)/(3x))(3-x)#?

Answer 1

Paisley Johnson

#-1 -1/x^2#

Combine the numerator by multiplying so that it is #(-3x^2+8x +3)/(3x)#

To differentiate now, use the quotient rule, or carry out the following steps:

#(-3x^2+8x +3)/(3x)# =#-x +8/3 +1/x#

Now differentiate term wise = #-1 -1/x^2#

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Answer 2

Samantha Adkison

To find the derivative of ((1+3x)/(3x))(3-x), you can apply the product rule. The product rule states that if you have two functions u(x) and v(x), then the derivative of their product u(x)*v(x) with respect to x is given by the formula: (u'(x)*v(x)) + (u(x)*v'(x)).

Let u(x) = (1 + 3x)/(3x) and v(x) = (3 - x).

Find u'(x) by applying the quotient rule, then find v'(x).

Once you have u'(x) and v'(x), plug them into the product rule formula to find the derivative of the given expression.

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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.