Find the first derivative of * An(In(In x)) 1 x In x (x In(In x)) In x In(In x) Option 2 Option 4 1 1 x In x In(In x) x In x In(x In x) Option 1 O Option 3

Q: O (CA)' = (cl*]) - [ca - [ca - cl27] - C(A') O (CA)T = (cle])" = [ca]' - [] = c[ed] = cta™) O (c4)T…

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Q: If f(x) = 6*, then f"(x) = A 6*(In6)3 B 6*(In6) (c) 6* 66 D (In6)3

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Q: (4) VL1, L2 ((L1 UL2)* = L₁* U L₂¹).

A: This is always True

Q: • prove that y` = = for y= (of (1+x)) 1+x²

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Q: The derivative of f(x) = x^x is * O x (1 + Inx) O (x^x) (1 + In x) O (1 + In x) O x (1 - In x)

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Q: (4³ + 6)%,' = x^(,5 + 6)5 y

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Q: Sx-² csc³ () cot () dx A) csc* (?) + c B) – ; csc° (*) + c c)금 csc* (2) + C D) – csc* () + c - 12 E)…

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Q: The residue of f(z)=1/(z+1)^3

A: f(z)=1(z+1)3

Q: If |z|=1,show that (z^-1) =(z congegate)

A: Given z=1 We have to show that z−1=z¯ Since, z=1 ⇒z2=1 We know that z2=zz¯

Q: 2-fx'e-2x* dx

A: To evaluate: I=∫x3e-2x4dx Substituting x4=u⇒4x3dx=du⇒x3dx=du4

Q: 1. Given the following graph and A(x)=f(t) dt, f , find: -2 -1 4 -3- --2- 1- 0 -1 --2- -3 1 2 3 5 6…

A: Given: To Find: To find .

Q: Evaluate x' V1+x? xp=

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Q: Rewrite y = 3 * (8) ^ (t / 15) in the form y^ prime =a(1+r)^ t or y = a(1 - r)

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Q: Suppose f" (x) = N,(h) + a,h? + azh* + azh6 + .. The value of N2(h) using Richardson's extrapolation…

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Q: Find the derivative y = e* In x In x ex E + e* In x O None of these

A: Use product rule:-

Q: Where is f(x) = e* continuous?

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Q: if fi(x) = xand f,(x,) = xf(x»x2) = Is this function independent true false

A: Function is independent if f(x1,x2) = f(x1) f(x2).

Q: The derivative of 01 COS I sin x esin(x) + ecos(x) et dt is - cos(x)esin(x) — sin(x)ecos(x)…

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Q: Suppose that the functions u and w are defined as follows. u (x) =-x-1 w (x) =? %3D Find the…

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Q: Let f(x) = In[2*(r + 5)*(=* - 4)"] f'(x) =

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