Consider the problem du + d = f (x), u = u (x) da? u' (0) = u (0) = (u' (1) + u (1)) Is the solution unique? Explain !

Q: A new graduate puts $1000 per year into a retirement plan mutual fund (at the beginning of each…

A: The sequence is…

Q: Find y' y= (x2+2)(x-3)

A: Given :                  y = x2+2x-3 Find :               y'

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

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

Q: Determine whether each case is true or not : * a. 44 = 13 (mod 3) > b. -55 = 5 (mod 4) → c. 74 = 1…

A: If a and b are integers and n > 0, we write a≡b(mod n) to mean n/(b-a). We read this as “a is…

Q: dy ху Solve dx (1+y2)

A:

Q: If f(x) = (5x +7)°, then the value of (f-1 (x))' at (f(-1),-1) is

A:

Q: 4 Use implicit differentiation to solve for y' if r4y2 - x³y + 2xy³ = (Show your work)

A:

Q: Calculate the derivative of the function. f(x) = [(2x – 1)2 + (1 – x)°]? %3D f'(x) = %D

A: We will find the derivative using chain rule.

Q: Find f'(2) if y = f(x) is the nonnegative function defined for x, y > 0 by the equation x" = y?.

A: To find f’ (2), if y = f (x).

Q: d csc 'x dx -1 Prove that xVx? – 1 2.

A:

Q: f(x) = 4x In(x), x> 0.

A:

Q: In f(x) dx = F(x). F(x) is called the

A: follow the procedure given below.

Q: H (x) = VI-Soe? 2. %3D (f09) (><)= H (sc) %3D %3D 9(36) =

A: Given fgx=1-5x2

Q: Find dy/dx if f(x) = csc (x³ + x + 1)

A: Derivative of the function

Q: If f(x) (1)? = 2 x² + 3x x+1 " then what is

A: Given: f(x)=x2+3xx+1

Q: Express [(XnY) U (XY)] in its simplest form.

A: We know, (A∩B)c=Ac∪Bc A-B=A∩Bc Sc=Φ, S is the universal set and Φ is the null set.

Q: Choose True if the statement is correct, otherwise False. If f(x)dx is to be integrated and u =…

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Q: goo3D 4X Sxt7

A:

Q: Let f(x) = 5x4 - -1/2+8√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the graph…

A: Given that            function f(x) = 5x4-2x2+8x-3     Now             f'(x)    =  ddx5x4-2x2+8x-3…

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

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Q: Differentiate the functions. a) f(x) = 2 – 3x + b) f(x) %3D Зе* + sinx c) f(x) = 3x

A: As per guidelines, we will solve only first three subparts. Kindly repost other subparts separately.

Q: x² – 9 Let f (x) -. Find and simplify f' (x) and f"(x). %3D Ax2 + B f'(x) = where A = |-4 B = 54 C =…

A: Given that two function we find its first derivative and also second derivative and after find value…

Q: If x = e*-Y then is equal to A) B) log z (1+log z)* C)

A: solution:-xy=ex-ytake log both sideslnxy=lnex-yylnx=x-ydifferentiate both sides w.r.t…

Q: Find the second derivatives, f"(x) of O a) b) f(x) = 2x² + e²² F"(x) = 2e² (4x²+4) F"(x) = 4+e²²(x²…

A: dxndx=nxn-1dexdx=exd dx(a.b)=a.dbdx+b.dadxf(x)=2x2+ex2

Q: If u(x) = x3, then du = 3x2.

A:

Q: 8 If x2 = 25 - y2, what is the value of dx2 a²y at the point (3, 4)? 25 (A) - 64 (B) - (C) (D) (E)…

A: use the quotient rule to find the second derivative.

Q: Given that f"(x) and f(1) = 3x² + 2x – 1 and f'(1) = 0 3, find f(x).

A: Given equation is f ”(x) =3x2 + 2x -1 f ’(1) = 0 f (1) =3