00:01
Our next question, you can see that we've got a cos term here,
so, we're going to be dealing with a little bit of trigonometry.
00:07
We are looking at differentiating cos y plus 2x to the 5 equals to 10.
00:13
If you try to rearrange this for y you're going to end up with some term with cos inverse
of a term which again has going to get messy,
so let's just stick with differentiating this implicitly.
00:26
Each term we have to differentiate, so, we're going to start with cos y,
remember firstly you're attempting to differentiate a y term
and secondly this also has trig, so, you need to remember
if you're differentiating cos y with respects to y.
00:43
Remember that cos goes to sine but this is going to go to minus sine y.
00:48
Apologies, coz goes to minus sine, so cos y becomes minus sine y
and then you multiply it with the factor of dy/dx
because it was a y term plus 2x to the 5, will differentiate to 10x to the 4,
when you bring the power down so you times it
and decreased the power by 1 equals to 10, which is a constant that just goes to zero.
01:11
All we have to do now is rearrange this equation,
so, if I leave the 10x to the 4 here and move the minus sine y to the other side,
that becomes positive sine y, dy/dx.
01:23
And then finally, 10x to the 4 over sine y equals to dy/dx.
01:31
So that's your gradient here, so you can substitute numbers and once again
to find what the particular gradient at different points will be.