Equation of Tangent - Quotient Rule

[AustrianSaurkraut]

For this question, I'm stuck on the numerator term and I really don't know what to do. Do I make the √x into x^1/2? Any help will be greatly appreciated.

Determine the slope of the tangent to the curve y= 55+√x/x²-3x-12 at the point where x = 4. Exact values only, as simplified as possible.

 

[Steven G]

√x/x² = x^1/2/x² = 1/x^3/2

So y' = -3/(2x^5/2)-3

y'(4) = -3/64 -3 =...

 

[Dr.Peterson]

For this question, I'm stuck on the numerator term and I really don't know what to do. Do I make the √x into x^1/2? Any help will be greatly appreciated.

Determine the slope of the tangent to the curve y= 55+√x/x²-3x-12 at the point where x = 4. Exact values only, as simplified as possible.

I would guess that you probably mean y= (55+√x)/(x²-3x-12)

Is that correct? That's [MATH]\frac{55+\sqrt{x}}{x^2-3x-12}[/MATH]; what you wrote is [MATH]55+\frac{\sqrt{x}}{x^2}-3x+12[/MATH]. In order to help fully, we need to be sure of that.

But, yes, the best way to differentiate a square root usually is to write it as a 1/2 power.

 

[skeeter]

duplicate post …

Equation of Tangent.

For this question, I tried to begin it but kept getting stuck with the numerator term. I'm unsure what to do from here, because the bottom denominator is not factorable. Would I use quotient rule by turning the √x to x1/2? But then I am left with a negative exponent. Any help will be greatly...

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