# How do you find #dy/dx# by implicit differentiation of #tan(x+y)=x# and evaluate at point (0,0)?

##### 2 Answers

At

#### Explanation:

When doing implicit differentiation, you follow these essential steps:

- Take the derivative of both sides of the equation with respect to
#x# . - Differentiate terms with
#x# as normal. - Differentiate terms with
#y# as normal too but tag on a#dy/dx# to the end. - Solve for the
#dy/dx# .

So, let's differentiate both sides:

The right hand side just comes out as

This comes out to:

Putting this back in the whole equation:

Now, you just solve for

Now, you're given the point

So your tangent line would have a slope of

If you want more help in implicit differentiation, check out my video:

Hope that helped :)

Evaluating at

#### Explanation:

Implicit differentiation is just differentiation using chain rule.

Rearranging:

Substituting

we get:

i.e