8. Iff₁=e¹x,f₂=e³x and fi,f2 and f3 are linearly dependent, the f3 could be (A) sin(3x) (B) ex (C) e 12x (D) ex-e4x (E) In (7x)

Q: 4. Find (f-1)'(1) if f(x)=x' +8x+sin(3.x) а. Find (f-1)'(2) if f(x)= Vx' +x +xr+1 b.

A: To find the derivative of the inverse of a function

Q: Let h(x) = 3x² + x -x² + 3x - 3 what is h' (2)?

A: We need to find out h'(2).

Q: Suppose h = f ∘ g. Find h'(0) given that f(0) = 6, f'(5) = -2, g(0) = 5, and g'(0) = 3.

A: It is given that

Q: f(æ) = cos(sin(x*)), then f'(x) =

A:

Q: If f(t) = e-t3 – 2 sin 2t determine L{f" (t)} %3D

A: Formula Used: L{eattn}=n!(s-a)n+1L{sin at}=as2+a2L{f''(t)}=s2L{f(t)}-sf(0)-f'(0)

Q: If 7'(t) = (cos t, e2t, 3t²) and r(0) = (3, 1, –2), find the function 7 (t).

A: Given. f'(t) = (cos t , e2t , 3t² ) To calculate the vector function are we need to integrate the…

Q: Find the differential of the following function: a) f(x) = x (2x³ + 9x)5 2t b) f(t) = (₁²₂)4 1-t2

A:

Q: If y = -cos(2t), then y(5)= ?

A:

Q: Let h(x) f(æ) If f(x) = 3 cos (x) and g(x) = 3x + 2x2 – x + 4, what is h' (x)? (æ)6

A: Given: f(x)=3cos(x)g(x)=3x3+2x2-x+4   Let h(x)=f(x)g(x).   Then, h(x)=f(x)g(x)=3cos(x)3x3+2x2-x+4

Q: If f(x) = 2 sin æ + 9 cos a, then f'(x) = f'(4) =|

A:

Q: Find f if f"(x) = 2+ cos(x), f(0) = 2, f(t/2) = -2.

A:

Q: s¯¹(x + 1) − √√14 − 3x², find ƒ¹(x). If f(x) = 3x cos

A:

Q: A 2xe ²x² B Xex² Ⓒ2e+² D 2xex² Let f(x)= ex², find f'(x)

A: given  f(x)=ex2d dx(ex)=exd dx(xn)=nxn-1

Q: F = If SF · dr = (5x − 3y²) dx + (x³y) dy, what is F?

A:

Q: If f(x) = cos(2x), then f"|

A:

Q: If f(x) = 2x cos ¹(x + 1) - √12-3x², find f'(x).

A: Introduction: Here use the derivative rules to solve the question.(1) Chain rule: (2) Power rule:

Q: Let f(x) 39 27 O 1 4√3 O-√6 9 3√3 .-1 (²). Then the second derivative at x = -1,f"(-1), equals = COS

A:

Q: In cof '3x sinAte ech x² 2

A:

Q: a) If f (x) = 12x, find f' (27). %3D

A: Solve the function

Q: Suppose that y varies directly as x' and inversely as w. If both x and w are doubled, what is the…

A: Given: y varies directly as x5 and inversely proportional as w2

Q: Provide the table of signs for both f' and ff'.

A: Given function is fx = x+334x-12 = x4 +12x-1+16x-12 +114. Also, given that f'x = x-9x+324x-13    and…

Q: 5. A function y = sin x is transformed into = -sin (3x) - 4. What is a possible transformation?

A:

Q: w= Cos (x+y) + Sin (X-4) Show that dy?

A:

Q: If f(x) = cos x, then f'() = A. B. - C. - C. D. √3

A:

Q: Take first and second derivatives of y = xr, y=(ax2 + bx + c)2, y=ecx, y=e-cx, y=ln(x).  In all…

A:

Q: F(s) = Le 4t cos(5t)}

A: We have to find  ℒe-4tcos5t Remember : ℒeatf(t)=Fs-a where  ℒf(t)=Fs

Q: IfI(u) = [log, (1-2u cos x+ u' )dx, then prove that, I(u)+I(-u)-DI(u²).

A:

Q: 7. Ax)= 2x' -5

A: We have to find

Q: a fif f" (t) = 2e* +3 sin(t), f(0) =-8, ) =

A:

Q: 1. ſ X (2x-5)² (3-4x) dx.

A: Solution: ∫x(2x-5)2(3-4x)dx Take the partial fraction ∫398(2x-5)-514(2x-5)2-349(4x-3)dx

Q: Suppose Im(f(z)) = 6x(2y -1) and f(0)= 3 -2i, f(1) = 6- 5i. Find f(1 + i)

A: Complex function

Q: 3. Suppose that f(1) = 2, f(4) 7, f'(1) 5, f'(4) = 3, and f" is continu- %3D | af" (x) da. ous. Find…

A: The given data is: f1=2f4=7f'1=5f'4=3  f'' is continuous  To find the value of ∫14xf''xdx.