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Find the differential dy of the following implicit functions: Find the differential dy of the following implicit functions: 1.y=tan(x+y) 2.y^2=x+lny
one
dy=[sec(x+y)]^2*d(x+y)
[cos(x+y)]^2*dy=dx+dy
-[sin(x+y)]^2*dy=dx
dy=-[csc(x+y)]^2*dx
two
d(y^2)=d(x+lny)
2ydy=dx+dy/y
(2y-1/y)dy=dx
dy=ydx/(2y^2-1)
Ordinary differential dy / DX = 1 / (x + y), find the general solution formula of this form and the representation of this function in the general solution formula
Let u = x + y
Then y '= u' - 1
Substitute into the original equation to obtain: u '- 1 = 1 / u
Get: Du / DX = (U + 1) / u
du*u/(u+1)=dx
du*[1-1/(u+1)]=dx
Integral: u-ln|u + 1| = x + C
That is, x + y-ln|x + y + 1| = x + C
I see the definition formula of differential dy = f '(x0) △ x, and the derivative can be expressed as dy / DX = f' (x0). Doesn't this simultaneous become DX = △ x First, is DX = △ x right? Second, how to understand it? I'm self-taught
If DX is involved, it means that the function must be differentiable. If it is △ x, it only represents infinitesimal quantities, which has nothing to do with whether the function can be differentiable or not. Therefore, △ x can be applied to some non differentiable functions
Delta X / deltay to approximate the substitution derivative, which is called difference
That is, if functions are differentiable, they are the same thing
Differential method ~ find dy / DX of e ^ x + e ^ y = x ^ 2 Differential method ~ find e ^ x + e ^ y = x ^ 2 Dy / DX of
e^x·dx+e^y·dy=2x·dx
e^y·dy=(2x-e^x)·dx
dy/dx=(2x-e^x)/e^y
Y = 6tan (x / 4) how to differentiate. Find dy / DX!
Let X / 4 = t, then y = 6tant, t = x / 4
Derivation formula from composite function:
dy/dx=dy/dt*dt/dx
=6sec^2(t)*(1/4)
=3/2*sec^2(x/4)
How do you read "d" of differential DX and Dy What is the pronunciation?
Our teacher reads the pronunciation of D in English
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