if sin x=e^y, 0

Question

if sin x=e^y, 0<x<pi, what is dy/dx in terms of x

ipwnbunnies · Answer

Take the derivative of both sides with respect to x.

ipwnbunnies · Answer

What's the derivative of sinx wrt x?

ipwnbunnies · Answer

It's easy. Just think of y as a function of x.

ipwnbunnies · Answer

Do you remember what the derivative of e^x is?

ipwnbunnies · Answer

...Another approach is the take the natural log (ln) of both sides to get rid of the e on the right side. You'll be left with ln(sin x) = y

anonymous · Answer

e^x right

ipwnbunnies · Answer

Ok yeah. Derivative of e^x is e^x.
How bout e^(2x)?

anonymous · Answer

2e^x * e^x

ipwnbunnies · Answer

That's a strange way to write it, but yes. Derivative of e^(2x) = 2e^(2x)

ipwnbunnies · Answer

So, what did we do here? We kept the original exponenial function, but found the derivative of the power with respect to x, and multiplied it. It is the same deal with your problem.

ipwnbunnies · Answer

$$\frac{d}{dx}[e^u] = e^u * \frac{du}{dx}$$

ipwnbunnies · Answer

So we have:
$$\cos x = e^y \frac{dy}{dx}$$

ipwnbunnies · Answer

Since the power isn't a term of x, we just write dy/dx.

anonymous · Answer

ok what d i do after tht