## m.auld64 2 years ago 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

1. experimentX

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

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

is that log base 2??

4. No-data

yes it is.

5. No-data

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

6. No-data

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