How do you find dy/dxdydx by implicit differentiation of tan(x+y)=xtan(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
xx . - Differentiate terms with
xx as normal. - Differentiate terms with
yy as normal too but tag on ady/dxdydx to the end. - Solve for the
dy/dxdydx .
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