How do you differentiate #(x-3)/(2x+1)#?

Answer 1

Charles Arocha

Quocient rule time!

By quocient rule's definition, we have:

#(dy)/(dx) = (f(x))/(g(x)) = (f'(x)*g(x) - f(x)*g'(x))/((f(x))^2)#

Now, let's just proceed:

#(dy)/(dx) = (1*(2x+1) - (x-3)*2)/(x-3)^2# #= (7)/(x^2-6x+9)#

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Answer 2

Isabella Ackerman

To differentiate (x-3)/(2x+1), you would use the quotient rule. The quotient rule states that if you have a function in the form of f(x)/g(x), the derivative is (f'(x)g(x) - f(x)g'(x)) / (g(x))^2. Applying the quotient rule to (x-3)/(2x+1), you would first find the derivatives of the numerator and denominator separately, then apply the formula to find the derivative of the entire expression. The derivative of the numerator (x-3) is 1, and the derivative of the denominator (2x+1) is 2. Substituting these derivatives into the quotient rule formula yields the final answer: (2 - 1) / (2x+1)^2. Simplifying this expression gives the derivative of (x-3)/(2x+1), which is 1 / (2x+1)^2.

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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.