How do you implicitly differentiate 2=e^(xy)cosy ?

1 Answer
Jun 7, 2016

y/(tan y - x)

Explanation:

You could differentiate right away, but to make things simpler let us take the natural logarithm on both sides:

ln 2 = xy + ln (cos y)

Differentiating with respect to x on both sides:

0 = y + x dy/dx + 1/(cos y) * (–sin y) * dy/dx
0 = y + x dy/dx - tan y * dy/dx
dy/dx = y/(tan y - x)