Let z = XY + YT and y = 2 ^ x, t = SiNx, find the total derivative DZ / dt 2x(2xln2+sinxln2+cosx+1)

Let z = XY + YT and y = 2 ^ x, t = SiNx, find the total derivative DZ / dt 2x(2xln2+sinxln2+cosx+1)

Let z = XY + YT and y = 2 ^ x, t = SiNx, find the total derivative DZ / dt
z=xy+yt,y=2^x,x=arcsint；
dz/dt=(∂z/∂x)(dx/dt)+(∂z/∂y)(dy/dx)(dx/dt)+(∂z/∂t)=y/√(1-t²)+[(x+t)(2^x)ln2]/√(1-t²)+y
Substituting y = 2 ^ x, t = SiNx, we get the following result:
dz/dt=(2^x)/√(1-sin²x)+[(x+sinx)(2^x)ln2]/√(1-sin²x)+2^x
=(2^x)(xln2+sinxln2+cosx+1)/cosx
Solution 2: you can do the same
Z = y (x + T) = (2 ^ x) (x + T), where x = arcsint
So DZ / dt = (&; Z / &; x) (DX / DT) + &; Z / &; t = [(2 ^ x) LN2 (x + T) + 2 ^ x] / √ (1-T &;) + 2 ^ x = (2 ^ x) {[LN2 (x + SiNx) + 1] / cosx + 1}
=(2^x)(xln2+sinxln2+cosx+1)/cosx .
Solution 3: z = y (x + T) = (2 ^ arxsint) (arcsint + T)
dz/dt=[(2^arcsint)ln2/√(1-t²)](arcsint+t)+(2^arcsint)[1/√(1-t²)+1]
=(2^x)ln2(x+sinx)/√(1-sin²x)+(2^x)[1/√(1-sin²x)+1]
=(2^x)ln2(x+sinx)/cosx+(2^x)(1+cosx)/cosx
=(2^x)[xln2+sinxln2+1+cosx)/cosx
=(2^x)(xln2+sinxln2+cosx+1)/cosx
Note: the answer you provided seems to be wrong!
What is the greatest common divisor and the least common multiple of 24 and 25
The greatest common divisor is 1 and the least common multiple is 24 × 25 = 600
∵ 24 and 25 have no common factor except 1 ∵ the maximum is 1, and the minimum common multiple is 24 × 25 = 600
The greatest common divisor is 1
The least common multiple is 600
If you think it's OK, take it_ ∩)O~
The greatest common divisor of 24 and 25 is 1, and the least common multiple is 24 * 25 = 600
Seeking the truth_ 0^y(e^t)dt+∫ _ The derivative of implicit function is determined by X / dt = 0.0
∫ _ 0 ^ y indicates that the upper limit is y and the lower limit is 0
The answer on the first floor is the same as my own, but the answer on the book is (cosx / sinx-1)
What the landlord and the first floor did is right, but you didn't find y (x);
Integral: ∫_ 0^y(e^t)dt=e^y-1
∫ _ 0^x(cost)dt=sin x;
E ^ y = 1-sin X;
y=ln(1-sin x);
dy/dx=cos x/(sin x-1)
The derivative of X is e ^ y * y '+ cos (x) = 0
Then y '= - cosx / e ^ y (x)
Find the greatest common divisor and the least common multiple of the following groups of numbers
(1) 5, 8 and 10
(2) 15, 18 and 30
(3) 24, 48 and 72
(1) The greatest common divisor of 5, 8 and 10 is (1), and the least common multiple is (40)
(2) The greatest common divisor of 15, 18 and 30 is (3), and the least common multiple is (90)
(3) The greatest common divisor of 24, 48 and 72 is (24), and the least common multiple is (144)
If you don't understand, please ask
Let z = XY + Sint, x = e ^ t, y = cost, and find the derivative DZ / dt
Ask for detailed answers
dz/dt=(xy)'+(sint)'
Here 'denotes the derivation of T
dz/dt=x'y+xy'+cost
=e^t*cost+e^t*(-sint)+cost
=e^t(cost-sint)+cost
If you don't understand, you can ask
Find the greatest common divisor and the least common multiple of each group of numbers below
(1) 54 and 36 (2) 13 and 39 (3) 11 and 37 (4) 18 and 82
(5) 12,42 and 46 (6) 15,27 and 90
（1）（54,36）=18 【54,36】=108
（2） (13,39) = 13 【13,39】=39
（3）（11,37）=1 【11,37】=407
(4) (18,82) =2 [18,82】=738
（5）（12,42,46）=6 【12,42,46】=1932
（6）（15,27,90）=45 【15,27,90]=270
Miss, this is not a sharp turn of the brain..
But it's OK to answer
1) Greatest common divisor 18 least common multiple 108
2) Greatest common divisor 13 least common multiple 39
3) Greatest common divisor 1 least common multiple 407
4) Greatest common divisor 2 least common multiple 738
5) Greatest common divisor 2 least common multiple 1932
6) Greatest common divisor 3 least common multiple 270
Not to unfold
Miss, this is not a sharp turn of the brain..
But it's OK to answer
1) Greatest common divisor of multiple 18 108
2) Greatest common divisor 13 least common multiple 39
3) Greatest common divisor 1 least common multiple 407
4) Greatest common divisor 2 least common multiple 738
5) Greatest common divisor 2 least common multiple 1932
6) Greatest common divisor 3 least common multiple 270
I have to say that the last few times I've been miscalculating. Put it away
Why is the derivative of y = Xe ^ x + 1 y '= e ^ x + Xe ^ x, and how to find the derivative of y = Xe ^ - x
y'=(xe^x)'+(1)=(x)'*e^x+x*(e^x)'+0=e^x+xe^x
Xe ^ X this is not two functions together, a set of formulas OK
What's wrong with this?
If it's this, it's very simple ← y '= Xe ^ x-x = e ^ x + Xe ^ X-1
What is the least common multiple of 12 and 15______ The greatest common divisor of; 12 and 15 is______ .
12 = 2 × 2 × 3, 15 = 3 × 5, so the greatest common divisor of 12 and 15 is 3, and the least common multiple is 3 × 2 × 2 × 5 = 60
Let z = sinxy + cos (x + y), then DZ=
I'll do it. Do me a favor,
dz=d(sinxy)+d(cos(x+y))
=cosxyd(xy)-sin(x+y)d(x+y)
=ycosxydx+xcosxydy-sin(x+y)dx-sin(x+y)dy
=[ycosxy-sin(x+y)]dx+[xcosxy-sin(x+y)]dy
How to find the greatest common divisor and the least common multiple?
For example, 12 and 20, 12 = 2 × 2 × 3, 20 = 2 × 2 × 5, and the factors shared by two numbers are two 2, so the greatest common divisor of 12 and 20 is 2 × 2 = 4