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richaeviney
01.11.2019 •
Mathematics
Which trigonometric identity was introduced in this unit?
a) sin^2 x= 1 + cos^2 x
b) (sin x + cos x)^2 = 1
c) tan x = sin x/cos x
d) tan x= cos x/sin x
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Ответ:
Ответ:
By the chain rule, if
, then
We have
, for which
•![\dfrac{\partial f}{\partial x} = e^y](/tpl/images/1409/3140/72a16.png)
•![\dfrac{\partial f}{\partial y} = e^y + (x+y)e^y = (x+y+1)e^y](/tpl/images/1409/3140/3cfec.png)
and
and
, so that
•![\dfrac{\mathrm dx}{\mathrm dt} = 5](/tpl/images/1409/3140/36e8a.png)
•![\dfrac{\mathrm dy}{\mathrm dt} = -2t](/tpl/images/1409/3140/a85fd.png)
Putting everything together, we get