### Home > APCALC > Chapter 6 > Lesson 6.4.3 > Problem6-155

6-155.

​ Write the equation of the line tangent to the graph of $e^{xy} + \ln(y) = 1$ at the point $(0, 1)$.

Use point-slope form. You are given the point.

$\text{Differentiate to find the slope, }\frac{dy}{dx}.$

$\frac{d}{dx}(e^{xy}+\ln(y))=\frac{d}{dy}(1)$

$\frac{dx}{dx}(e^{y})+\frac{dy}{dx}(e^{x})+\frac{dy}{dx}\left(\frac{1}{y}\right)=0$

$\frac{dx}{dx}(e^{y})+\frac{dy}{dx}\left(e^{x}+\frac{1}{y}\right)=0$

$\text{Now solve for }\frac{dy}{dx}.$

Evaluate at the given point.