Question

if sin x=e^y, 0 12 years ago

Answer 1

Take the derivative of both sides with respect to x.

Answer 2

What's the derivative of sinx wrt x?

Answer 3

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

Answer 4

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

Answer 5

...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

Answer 6

e^x right

Answer 7

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

Answer 8

2e^x * e^x

Answer 9

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

Answer 10

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.

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

ok what d i do after tht