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## m.auld64 Group Title use implicit differentiation to find the slope of the tangent line to the curve 3^x + log_2(xy) = 10 at the point (2,1) and use it to find the equation of the tangent line in the form y = mx + b 2 years ago 2 years ago

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1. experimentX Group Title

differentiate it and get the differential equation 3^x*ln(3) + 1/(xy)*{1+xdy/dx} = 0 find value of dy/dx which is .. roughly -21 http://www.wolframalpha.com/input/?i=3%5E2*ln%283%29+%2B+1%2F2%281%2Bx%29+%3D+0 which is the slope of the tangent, since you know slope m, and you have point (2,1) find the value of b, you have your tangent

2. experimentX Group Title

oops sorry, slope is around -1.05 http://www.wolframalpha.com/input/?i=3%5E2*ln%283%29+%2B+1%2F%282%281%2Bx%29%29+%3D+0

3. experimentX Group Title

is that log base 2??

4. No-data Group Title

yes it is.

5. No-data Group Title

I got this: $(\ln 3)3^x+\frac{1}{(\ln 2)xy}\left(x\frac{dy}{dx}+y\right)=0$

6. No-data Group Title

you can solve for $\frac{dy}{dx}$ and substitute the coordinates given. so you'll have the slope.