Under normality, prove the followings (a) B~ N(B,0²(X'X)-)

Q: x if x20 If Ax) = -x2 then f'(0) if x <0

A: Given function, fx=x2      if x≥0-x2   if x&lt;0

Q: 6) Let h(x) = x7 + 2x +. Find h'(x).

A:

Q: -1 if f(x) = xtan ,"x,find f' (/3 )by first principle

A:

Q: Suppose that f(x) Evaluate each of the following: f'(3) = %3D f'(-1) =

A: Given function is : fx=3x9 The given function can be written as : fx=3x-9

Q: (b). Use the definition of the derivative to evaluate f (x)=x". [Hint: Use the Binomial Theorem:…

A: Given: i. fx=xnii. a+bn=an+nan-1b+nn-12!an-2b2+·····+nabn-1+bn. To Find: Use definition of…

Q: Let f(æ) = In a*(x + 5)*(2² + 4)*| f'(x) =

A: We will use properties of logarithm. lnan = n lna  ln(a.b) = lna + lnb

Q: 7) Find f(e) if a) f'(;) = { x and f6)=2 D f'(x)=\+sinx & f 3.

A: Here we find the f(x) using integration.

Q: Let f(x) = – 5 In(7x) f'(x) =

A: Given,           fx=-5ln7x

Q: Let f(x) f'(2)= | ƒ' (6)= Lomm 7 Vx Evaluate each of the following: I

A:

Q: Let f(t) = 3t – 8t + 5e'. - Then f'(t) =

A:

Q: Let 7(t) = Find (t) 7' (t) =

A: Given query is to find the derivau of r(t).

Q: '5 Find | f(x) dx if 3 if x < 3 f(x) %3D if x 2 3.

A:

Q: Use the definition of the derivative to evaluate f(x)=x". [Hint: Use the Binomial Theorem: (a+b)" =…

A: Consider the give function fx=xn

Q: -1 Ax) = 7xsin (x) f'(x) =

A: SOLUTION-

Q: 1) If f(x) = x²(2), find f'(2)

A: f(x)=x2∫2xdtt2+5we know  d dx(∫axf(t)dt)=f(x)×d dx(x)-f(a)×d dx(a)

Q: Let 7(t) = Find 7'(t) 7 (t) =

A: Topic - vectors and derivatives Since r→t = 5 t5-1, -e-t, -3 sin2t we to find r→'t  derivative of tn…

Q: Let f(x) = 6x4 In(x) + 3 ,5 2. 5 f'(x) = ||

A: The objective is to find the derivative.

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: - 3 Let f(x) = 8xVæ + x2. f'(x) =

A: Use the derivative for finding the answer.

Q: Suppose that f(x) = x2 + 17 Find f' (1). f'(1) =|

A: The function fx=exx2+17. We have to calculate the value of f'1.

Q: Let F(2) = 2, F'(2) = 3, H(2) = 4, H'(2) = 3. A. If G(z) = F(z)*H(z), then G'(2) = _______ B. If…

A: The Product Rule:The Quotient Rule:

Q: prove that P(X)=P(X|F)P(F) + P(X|F')P(F')

A:

Q: Let 7(t) = Find 7'(t) F'(t) =

A: The objective is to find the derivative of given

Q: Let f(x) = V4 – 8. - f-'(x) =

A:

Q: Let I +1 f(z) = I + 10 f(- 5) :

A:

Q: - 7t? - 6t + 2' 7t² –1'3t³ + 7 7 7t Let r(t) = Find r'(t) F'(t)

A:

Q: Let f(x) = – 4logs (æ) f'(x) = f'(4) =

A: Given,           fx=-4log8x

Q: Let 7(t) = Find 7'(t) デ'() = Answer preview:

A: We have to solve