# Thread: Finding a Tangent Line

1. ## Finding a Tangent Line

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.

2. ## Re: Finding a Tangent Line

$\frac{dR}{dx}$ is the slope of the curve at any point $(x,R)$ on the curve ...

evaluate the derivative at $x = 1$ , $R = 1$ to find the slope of the tangent line at that specific point, then use the point-slope form of a linear equation ...

$R - R_1 = m(x - x_1)$

3. ## Re: Finding a Tangent Line

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)

4. ## Re: Finding a Tangent Line

That is not the derivative. Since R is a function of x, you will need to use implicit differentiation.

5. ## Re: Finding a Tangent Line

$x^3 \cdot R^5 = 1$

solve for $R$ in terms of $x$ ...

$R = x^{-\frac{3}{5}}$

... now find $\frac{dR}{dx}$

6. ## Re: Finding a Tangent Line

so the derivative would actually be:

dr/dx = -3/(5*x^(8/5))

7. ## Re: Finding a Tangent Line

ok ... find the equation of the tangent line.

8. ## Re: Finding a Tangent Line

so the equation should be:

R - 1 = -3/5(x-1)