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How do you differentiate #(3x-4/x)^2 (1-x+7x^2)^4#?

Answer 1

Scarlett Allison

#2(3x - 4/x^2) (3 + 4/x^2)[(1 - x + 7 x^2)^4] +(3x - 4/x^2)^2[4(1 - x + 7 x^2)^3(-1 + 14x)#

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Answer 2

Cameron Alexander

To differentiate the expression ((3x - \frac{4}{x})^2 \times (1 - x + 7x^2)^4), you would use the product rule of differentiation. The product rule states that if you have two functions, (u(x)) and (v(x)), then the derivative of their product, (u(x) \times v(x)), is given by (u'(x) \times v(x) + u(x) \times v'(x)), where (u'(x)) and (v'(x)) represent the derivatives of (u(x)) and (v(x)) with respect to (x), respectively. Applying this rule to the given expression, you would differentiate each part separately and then combine the results using the product rule.

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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.