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

What I have:
$
sec^2(x+y) (1+y') = (1)$

$
sec^2(x+y)+y'sec^2(x+y)
$

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

however, the answer for the first part is $-sin^2(x+y)$. 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 $dy/dx$ by implicit differentiation and evaluate the derivative at the given point"
$tan (x+y) =x , (0,0)$

What I have:
$
sec^2(x+y) (1+y') = (1)$

$
sec^2(x+y)+y'sec^2(x+y)
$

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

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

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

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

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

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

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