# Thread: Need help with implicit differentiation

1. ## Need help with implicit differentiation

Hi, I'm having an issue using implicit differentiation. I don't think I'm doing it correctly on the first step.

Equation: "Find $\displaystyle dy/dx$ by implicit differentiation and evaluate the derivative at the given point"
$\displaystyle tan (x+y) =x , (0,0)$

What I have:
$\displaystyle sec^2(x+y) (1+y') = (1)$
$\displaystyle sec^2(x+y)+y'sec^2(x+y)$
$\displaystyle y'=\frac {1-sec^2(x+y)}{sec^2(x+y)}$

however, the answer for the first part is $\displaystyle -sin^2(x+y)$. Thanks in advance.

2. Originally Posted by cynlix
Hi, I'm having an issue using implicit differentiation. I don't think I'm doing it correctly on the first step.

Equation: "Find $\displaystyle dy/dx$ by implicit differentiation and evaluate the derivative at the given point"
$\displaystyle tan (x+y) =x , (0,0)$

What I have:
$\displaystyle sec^2(x+y) (1+y') = (1)$
$\displaystyle sec^2(x+y)+y'sec^2(x+y)$
$\displaystyle y'=\frac {1-sec^2(x+y)}{sec^2(x+y)}$

however, the answer for the first part is $\displaystyle -sin^2(x+y)$. Thanks in advance.
same thing ...

$\displaystyle \frac{1-\sec^2(x+y)}{\sec^2(x+y)}$

multiply numerator and denominator by $\displaystyle \cos^2(x+y)$ ...

$\displaystyle \frac{\cos^2(x+y) - 1}{1}$

$\displaystyle -[1 - \cos^2(x+y)]$

$\displaystyle -\sin^2(x+y)$