1. ## implicit differentiation help

I got a complete different answer from any of the choices, can anyone lead me to the right direction as to get an answer to this?

I ended up with xe^6x/cos(x+6y)-1/6, any help would be appreciated you thank :]

same as this one,

I ended up with e^x(x^2-2x+6)+e^x(2x-2)

2. for the second one, factor $\displaystyle e^x$ out, and combine like terms to get your answer

3. Originally Posted by tecknics
I got a complete different answer from any of the choices, can anyone lead me to the right direction as to get an answer to this?

I ended up with xe^6x/cos(x+6y)-1/6, any help would be appreciated you thank :]

same as this one,

I ended up with e^x(x^2-2x+6)+e^x(2x-2)
Outside of the $\displaystyle x$ in red (above) I agree with you. For the second, factor and $\displaystyle e^x$ and you'll see an answer given.

4. i got the second one, rather easy dunno how i missed it, but as far as the first one goes im still lost :[

5. Differentiating gives

$\displaystyle 6 e^{6x} = \cos(x+6y)(1 + 6y')$

so

$\displaystyle 1+6y' = \frac{6e^{6x}}{\cos(x+6y)}$

or

$\displaystyle y' = \frac{e^{6x}}{\cos(x+6y)} - \frac{1}{6}.$

6. Originally Posted by Danny
Differentiating gives

$\displaystyle 6 e^{6x} = \cos(x+6y)(1 + 6y')$

so

$\displaystyle 1+6y' = \frac{6e^{6x}}{\cos(x+6y)}$

or

$\displaystyle y' = \frac{e^{6x}}{\cos(x+6y)} - \frac{1}{6}.$
Yes, i got that answer excluding my previous x, but its not an option on one of the given responses could the responses given to me be incorrect?