# Thread: Chain rule for exponential functions

1. ## Chain rule for exponential functions

I have a question I could use a little help with here...

Find the equation of the tangent to the function f(x) = 3^(x^2+1) - x^2 at (1 , 8)

I have used the difference rulwe and the chain rule for exp. functions to come up with the derivative:

2x(3^(x^2+1)) (ln3) - 2x

So using 1 for the value of x I come up with m = 17.77

I have the solution to the question which shows one of the last few steps of the solution as:

y = 17.77(x-1) + 8

If the formula for the equation is y = mx + b.... Why does the solution have (x - 1) as the x value. And how did they come up with 8 as the y - intercept? Thanks!

2. If you know that the equation for a line has slope m, and that it passes through the point (x1, y1), then it's equatoin is:

$\displaystyle \frac {y - y_1} {x - x_1} = m$

or rearranging:
$\displaystyle y - y_1 = m(x-x_1)$

So here you have:

y-8 = 17.77(x-1)

Which you can rearrange into y = mx+b form:

y = 17.77(x-1) + 8.
y = 17.77x -9.77

The y-intercept of the line is therefore: -9.77

3. Originally Posted by ebaines
If you know that the equation for a line has slope m, and that it passes through the point (x1, y1), then it's equatoin is:

$\displaystyle \frac {y - y_1} {x - x_1} = m$

or rearranging:
$\displaystyle y - y_1 = m(x-x_1)$

So here you have:

y-8 = 17.77(x-1)

Which you can rearrange into y = mx+b form:

y = 17.77(x-1) + 8.
y = 17.77x -9.77

The y-intercept of the line is therefore: -9.77
Got it. Thanks!