How can I go about finding a tangent line for the following: (x^3)*(R^5)=1 at the point (x,R)=(1,1) I took the derivative of the equation but I didn't know where to go after that.
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is the slope of the curve at any point on the curve ... evaluate the derivative at , to find the slope of the tangent line at that specific point, then use the point-slope form of a linear equation ...
So if I take the derivative I get: 3*R^5*X^2 Then if I evaluate that at x=1, R=1 I get: 3*1^5*1^2 = 3 So the point slope of the linear equation should be the following: R - 1 = 3 ( X - 1)
That is not the derivative. Since R is a function of x, you will need to use implicit differentiation.
solve for in terms of ... ... now find
so the derivative would actually be: dr/dx = -3/(5*x^(8/5))
ok ... find the equation of the tangent line.
so the equation should be: R - 1 = -3/5(x-1)
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