anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
im not really sure how to differentiate this if anyone could explain that to me
experimentX
  • experimentX
your differeantiation is 3^3*ln(3) + 1/(xy)*{1+xdy/dx} = 0 find the value of dy/dx form here, put the value of m = dy/dx on slope, and put the value of x,y on the that eqn of tangent, find the value of b, you have your tangent
anonymous
  • anonymous
i really don't think i know how to solve for dy/dx my professor just started implicit differentiation and I'm lost on this stuff

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experimentX
  • experimentX
okay differentiate this equation x^2+y=0
anonymous
  • anonymous
2x+1=0
experimentX
  • experimentX
no ... it's 2x+dy/dx = 0, here y is a variable that depends on x,
experimentX
  • experimentX
of course you can see that, y = -x^2, which is a parabola, on this particular case, you can separate y, but this is not always the case
anonymous
  • anonymous
ok so still how exactly do i get dy/dx by itself
experimentX
  • experimentX
differentiate this wrt x y = -x^2
experimentX
  • experimentX
you can differentiate y using chain rule, for eg you have x^2+y^2 = 25, try differentiating this
anonymous
  • anonymous
2x+2y(dy/dx=0
anonymous
  • anonymous
2x+2y(dy/dx)=0
experimentX
  • experimentX
yes, so you have differential equation, though you don't know that is y, you can find slope of tangent at given point okay, what is slope of tangent at (0,5)
anonymous
  • anonymous
the actual act of differentiating its figuring out how to separate the dy/dx to the other side in order to solve for it
experimentX
  • experimentX
i wouldn't say solving it though, you can find the function for slope of tangent of given curve
anonymous
  • anonymous
I'm sorry, I'm not sure what you mean
experimentX
  • experimentX
f(x,y) = 0 gives a curve in x,y plane .. i guess you know that
anonymous
  • anonymous
so I'm getting the slope as -10.05 when i plug in my x and y
experimentX
  • experimentX
yeah, you get it because you know the FUNCTION OF SLOPE, and PUTTING x,y in FUNCTION GIVES the value of function, which is slope and also, you know that dy/dx gives the tangent ... right, so it must the the slope of tangent ... now you know it!!!

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