Question

The slope of the tangent line to the curve y(cos x)+e^y=5 at the point where x=pi/2

Answer 1

Have you considered calculating dy/dx via the implicit derivative?

Answer 2

how to do that,,,?

Answer 3

product rule and chain rule

Answer 4

\[ y\cos (x)+e^y=5\]
\[y'\cos(x)-y\sin(x)+e^yy'=0\] solve for \(y'\)

Answer 5

what do i do with the y when i solve for y'?

Answer 6

y(cos x)+e^y=5

plug in x=pi/2 and solve that for y.

Then plug x=pi/2 and that above y value into the y' equation.