# Thread: derivitive help

1. ## derivitive help

Having issue with e^x problems. example:

ye^x - xe^y = xy find (a) dy/dx and (b) d^2y/dx^2

I'd likely not have issue with the second derivitive if I could figure the first.

the xy is easy, just product rule. the other side, however, I'm not sure how to get dy/dx. Is it simply dy/dx ye^x - d/dx xe^y and then you can just use the product rule? If someone can work that out, I can figure out what you did.

also:

y=3e^(x^(2-1))*x^(x-1) find y'. I can even begin to describe where I get lost there.

and:

lim x->0 (e^-x-1)/(1-e^x)

I can do these with non e^x but these are the only ones that are throwing me off. Thanks for any help!

2. Originally Posted by BooGTS
Having issue with e^x problems. example:

ye^x - xe^y = xy find (a) dy/dx and (b) d^2y/dx^2

I'd likely not have issue with the second derivitive if I could figure the first.

the xy is easy, just product rule. the other side, however, I'm not sure how to get dy/dx. Is it simply dy/dx ye^x - d/dx xe^y and then you can just use the product rule? If someone can work that out, I can figure out what you did.

also:

y=3e^(x^(2-1))*x^(x-1) find y'. I can even begin to describe where I get lost there.

and:

lim x->0 (e^-x-1)/(1-e^x)

I can do these with non e^x but these are the only ones that are throwing me off. Thanks for any help!
The dirivative of $e^x$ is $e^x$ !

When differentiating with respect to x, $\frac{d}{dx}e^y=e^y\frac{dy}{dx}$

It's that easy!

So your problem $ye^x-xe^y=xy$

You've gotta use the power rule in each term so that

$(ye^x+e^x\frac{dy}{dx})-(xe^y\frac{dy}{dx}+e^y)=(x\frac{dy}{dx}+y)$

3. Originally Posted by BooGTS
Having issue with e^x problems. example:

ye^x - xe^y = xy find (a) dy/dx and (b) d^2y/dx^2

I'd likely not have issue with the second derivitive if I could figure the first.

the xy is easy, just product rule. the other side, however, I'm not sure how to get dy/dx. Is it simply dy/dx ye^x - d/dx xe^y and then you can just use the product rule? If someone can work that out, I can figure out what you did.

also:

y=3e^(x^(2-1))*x^(x-1) find y'. I can even begin to describe where I get lost there.

and:

lim x->0 (e^-x-1)/(1-e^x)

I can do these with non e^x but these are the only ones that are throwing me off. Thanks for any help!

$lim_{x\rightarrow 0} \frac{e^{-x}-1}{1-e^x}$

$lim_{x\rightarrow 0 } \frac{\frac{1}{e^x} - 1 }{1-e^x }$

make the denominator in the numerator the same ( I do not know what you called this operation ) after you do that it will be easy

4. Originally Posted by BooGTS
y=3e^(x^(2-1))*x^(x-1) find y'. I can even begin to describe where I get lost there.
I will solve an example similar to your question

$y=4e^{x^2}(x^{\sin x})$

$y'=4\left(\frac{d}{dx}e^{x^2}\right)(x^{\sin x})+4\left(\frac{d}{dx}(x^{\sin x})\right)(e^{x^2})$

$y'=4(2xe^{x^2})(x^{\sin x})+4(\cos x)(ln(x)(x^{\sin x })(e^{x^2})$

$y'=(8xe^{x^2})(x^{\sin x})+4\ln (x)(\cos x)(x^{\sin x })(e^{x^2})$

note that

$\frac{d}{dx} x^{f(x)} = f'(x) ln(x)x^{f(x)}$ f(x) is a function

$\frac{d}{dx} e^{f(x)} = f'(x) e^{f(x)}$