# Thread: implicit differentiation with e

1. ## Derivative with log

hi everyone i am having troubles answering this question:

Determine the equation of the tangent line at the indicated -coordinate.
for .
The equation of the tangent line in slope-intercept form is

PS. I am allowed to use the calculator for this problem
I also posted the wrong title
Thank you..

2. ## Re: implicit differentiation with e

We have: $e^{9x}\cdot~e^{14y}=9y^2+x$

Differentiating the left as a product, we get:

$\frac{d}{dx}(e^{9x})\cdot~e^{14y}+\frac{d}{dy}(e^{ 14y})\cdot (\frac{dy}{dx})\cdot{e^{9x}}=\frac{d(9y^2+x)}{dx}$

Can you take it from here? If not, please show your method.

3. ## Re: Derivative with log

Originally Posted by danicloud
hi everyone i am having troubles answering this question:

Determine the equation of the tangent line at the indicated -coordinate.
for .
The equation of the tangent line in slope-intercept form is