Find the solution of the following IVP x²y' + 2xy = ln(x), y(1) = 2 1 1 y = ln(x) y=-In(x) - + 3/2 - X x2 X11 + X|N - 2 x² -2

Q: 3. x³y' = x²y—y³ { 2 1 x 2 = ln|x|+c} 2

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Q: If f' (4) = -9 and g ' (4) = -5, find (a) h'(4), if h(x) = 10f(x) + 2. %3D h'(4) = %3D (b) F'(4), if…

A: Recall: (αf(x)±βg(x))' = α f'(x)±β g'(x) ; where α and β are real numbers.

Q: If f(x) = 10x +64 then f'(x) = * 10 О 64 O 10x

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Q: If y = (4x + 7), find y' (1). O 11 ln(11) + 4 O 11 ln(11) O - O 11 ln(11) - 4 In(11) – - In(11) + 4…

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Q: Let h(x) = f(x) = g(x). If f(x) = 9x² and g(x) = 8x, what is h'(-5)? - Do not include "h' (-5) =" in…

A: SOLUTION-

Q: Suppose that f(2) = -3, g(2) = 2, f '(2) = -4, and g'(2) = 5. Fir (a) h(x) = 5f(x) – 4g(x) h'(2) =…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: If f(x)=4x2-2x+3 solve f'(x)=28

A: We first find f'(x) using exponent rule: [d/dx(x^n)= n*x^(n-1)]

Q: If q (x) = ln (6x² + 2x+2), find q' (x). O 12x + 2 In(6x² + 2x + 2) O 3x² + x + 1 6x +1. 6x +1…

A: The given function qx=ln6x2+2x+2 use  the derivative formulas, ddxxn=nxn-1ddxa=0ddxln…

Q: 3x + 7 If f(x) = find: %3D 3x + 5 f'(x) = %3D f'(1) =

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Q: 5x2 + 8x + 4 If f(x) = then: 15x2 + 8x - 4 f'(x) = %3D 3 2x f'(1) = %3D

A: Given that  f(x) =5x2+8x+4xTo find : f'x and f'1

Q: 1. Find f'(x) for f(x) = ln x + 2e - 3x².

A: The given function fx=ln x+2ex-3x2. We have to find the derivative function f'x.

Q: 4x + 6 If f(x) = find: 7x + 4 f'(x) = %3D f'(1) =

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Q: What's the limit function f(x) = lim fn(x),

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Q: Graph. -2x - 1 if x 1

A: The given function is f(x)=-2x-1;  if   x<-1        1    ;  if-1≤x≤1    2x-1;  if   x>1 Obtain…

Q: If g(x)=(2x+9)^15 (6x+5)^25 Find g'(x)=

A: Given:gx=2x+9156x+525We need to find g'x. i.e., dgdxWe will use the following formulas:ddxxn=nxn-1;…

Q: 1. If f(x) = 5x4 - 6x² + 4x - 2 find f'(x) and f'(2).

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Q: 9-16 Find f'(x). 1 9. f(x) = x-3+ x7 %3D 11. f(x) = -3x-8+2x %3D

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Q: If f(4) = 5 and f'(x) 2 2 for 4 s xS 9, how small can f(9) possibly be? %3D

A: Mean Value Theorem   Let f(x) be a function that satisfies the following hypotheses: a) f(x) is…

Q: if f(x) = 3x+4 over 4x+3 then f'(x)=?

A: Given: fx=3x+44x+3 To Find: f'x=?

Q: If g(x) = %3D 4 - x2 then .? Select one: 8x2 O g (x) = (4 – x2)2 8x O g (x) = 4 - x2 8x O g (x) = (4…

A: We will solve the problem

Q: 1 64 + 4f(1) + 7z²(f(x))* = 0 and f(1) = -2, find f'(1).

A: Given:

Q: x2 f(x) = + 4 %3D x2 - 4 Find f'(x) and f"(x). -16x (,² – 4)² f'(x) %3D 2 f"(x)

A: Recall: Quotient Rule of differentiation : ddxuv =vdudx-udvdxv2 dxndx=nxn-1

Q: 1. If f(x)=−1(7x^2−4)^3 then f′(x)= and f′(−2)=

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Q: If f(x) = f'(x) = f'(1) = 7x + 5 6x + 2 3 find:

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Q: If ln x + ln(x − 3) = ln(7x), then z

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Q: x) [in(3x²-36)]². Then f'(x) = A. 12x In (3x²-36) 3x²-36 O A. O B. O C. O D. O E. 2 In (3x²-36)…

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