00:01
So in this question, we want to find the equation of the tangent plane to the surface z equals e to the x plus y plus y plus y, plus 2 at the point 0471.
00:12
So what do i do? well, the equation of a tangent plane, you may recall, can always be written in the following form.
00:21
It can be written in the form of z minus z -0 is equal to my partial of f with respect to x, at the point x -not y -not times the quantity of x minus x not plus the partial of f with respect to y at the point x -not y times the quantity of y minus y not so i'm going to need my partials of z with respect to x and y so what is my partial of z with respect to x well the derivative of e to the x with respect to x is just e to the everything else differentiates to zero here, and so my partial of z with respect to x is just e to the x.
01:15
If i evaluate my partial of z with respect to x at the point that i've been provided, 0 -471, i'm just getting e to the zero power, which is one.
01:32
Now i also need my partial of z with respect to y.
01:38
The derivative of e to the x with respect to y, that's just zero.
01:42
While the derivative of y plus y cubed with respect to y, that's one plus three y squared, of course the two that differentiates to zero as well...