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How do you find the derivative of #v=4(2x^2-x+3)^-2#?

Answer 1

Ezekiel Alexander

#dv/dx=-8(4x-1)(2x^2-x+3)^-3#

differentiate using the #color(blue)"chain rule"#

#"Given " f(x)=g(h(x))" then"#

#• f'(x)=g'(h(x))xxh'(x)#

#rArr(dv)/dx=-8(2x^2-x+3)^-3xxd/dx(2x^2-x+3)#

#color(white)(rArrdv/dx)=-8(4x-1)(2x^2-x+3)^-3#

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Answer 2

Axel Alvarez

To find the derivative of ( v = 4(2x^2 - x + 3)^{-2} ), use the chain rule. The derivative is:

[ \frac{dv}{dx} = -8(2x^2 - x + 3)^{-3}(4x - 1) ]

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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.

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