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How do you find the derivative of #g(t)=t^2-4/t^3#?

Answer 1

Samantha Adkison

#g'(t)=2t+12/t^4#

Express g(t) in the following form.

#g(t)=t^2-4t^(_3)#

differentiate each term using the #color(blue)"power rule"#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(ax^n)=nax^(n-1))color(white)(2/2)|)))#

#rArrg'(t)=2t+12t^(-4)=2t+12/t^4#

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Answer 2

Luke Alvarez

To find the derivative of ( g(t) = t^2 - \frac{4}{t^3} ), you can use the power rule and the quotient rule.

The derivative of ( t^2 ) with respect to ( t ) is ( 2t ).

For the second term, ( -\frac{4}{t^3} ), using the power rule, the derivative is ( 4t^{-4} ).

Now, combining the derivatives of both terms, the derivative of ( g(t) ) is ( g'(t) = 2t + 4t^{-4} ).

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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.