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How do you differentiate #(4x^-2) - 8x + 1#?

Answer 1

Emilia Aguilar

#y'=-8x^-3-8#

#y'=4(x^-2)'-8(x)'+(1)' = 4*(-2)*x^(-2-1) - 8*1 + 0#

#y'=-8x^-3-8#

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Answer 2

Emma Aldridge

To differentiate the expression (4x^-2) - 8x + 1, we apply the power rule and the constant rule of differentiation.

Differentiating each term separately:

For the term 4x^-2, we use the power rule which states that if we have a term of the form ax^n, its derivative is nx^(n-1). So, the derivative of 4x^-2 is -8x^-3.
For the term -8x, the derivative of a constant times x is simply the constant itself. Therefore, the derivative of -8x is -8.
For the constant term 1, its derivative is always 0.

Putting it all together, the derivative of the expression (4x^-2) - 8x + 1 is: -8x^-3 - 8.

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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.