1. Let ?g(x) =1/(x^2)+1 . 1.1 With h= 0.002, use the forward, backward and central difference formula to approximate g'(0.5) .

Q: 8/7 Find g'(x) for g(x)=x g'(x) =

A: The given function is

Q: Compute backward difference approximations for the first derivative of the function, y =[ e'nxP, at…

A: We have to compute backward difference approximations for the first derivative of the function,…

Q: Evaluate the second derivative of e e22.1.png acos(b/x) f(x) = x2 if a = 123 and b = 0.5 at x = 6…

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Q: Given f (10) = 4 and f '(10) 8 find the value of h'(10) based on the function below. h(x) = (f(x))³

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Q: Find the derivative of the function. (a) g(x) - log,(8x - 9x²) - (x),6 (b)

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Q: Given the table of values below, find h'(1) if h(x) = Xx 1 f(x) 1 g(x) (x) 2 f'(x) 3 g(x) -3 g'(x)…

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Q: Differentiate g(ar) = In (7 7-x g'(x) = 0

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Q: Find g'(4) given that f(4) = -10, f'(4) = -9, and g(z) = Vif(x). %3D

A: Consider the handwritten solution.

Q: Let f(1) = 2 and f' (1) = 3. Suppose g(x) = [f(x)5"]. Calculate g' (1).

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Q: For the function f(x) = find f'(x). Then find f''(0) and f'"(4). 6 + x' f'"(x) = Select the correct…

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Q: A developing country's gross domestic product (GDP) from 2006 to 2015 is approximated by the…

A: Given: The GDP of a country is given using the function: Gt=-0.3t3+3.6t2+54 (a) Firstly find the…

Q: g'(2) = g(x) = x + 4

A: dxndx=nxn-1g(x)=x+4x2g(x)=x+4x-2

Q: Find the derivative of the function. Y= q56* In(2)ln(5)ln(6)· 3*. 5".; 2:56*+1+x

A: Given problem:-

Q: d steps for each problem

A: Here we have to find the derivative of  1) f(x)=e-x2 2) f(x)=ln(x3-5)2 3) f(x)=lnex

Q: Calculate G' (-4) to 3 significant figures where G(x) = (-4x – 2)'°(-2x² + 1x + 4)12

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Q: Use the information in the table to find h'(a) at the given value of a. h(x) = (- 2 f(x) ;a = 3 g(x)…

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Q: 1. f(X)= xpi - pi(x) + pi/x + pix - cos (pi)

A: Given, fx=xπ-πx+πx+πx-cosπ We know that dxndx=nxn-1daxdx=axlnx

Q: 1/5 Find g'(x) for g(x) = x

A: The given function g(x)=x15 Use differentiation formula dxndx=nxn-1 Here, n=1/5 n-1=15-1=-45

Q: - 3/7 Find g'(x) for g(x) = x g'(x) =

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Q: Find g'(6) given that f(6) = -3, f'(6) = 4, and g(x)= g'(6) = -91.6667 X = 9x + 8 f(x) (Round your…

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Q: Find the first and second derivatives of the function. 16 L(t) = 1+2.leS L'()=-16(1+2.1*)*(2.10*)…

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Q: Determine h' (x) when it is given that [h(2x)] 16

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.