f(x) = ex, using different values for h = 10− 1, 10− 2, .. . , 10− 9.

Q: A function is given as x - 6y = 5– x. Calculate the derivative of y with respect to r with two…

A:

Q: 2. find the high er order derivative of the given funcion witch whi ch Equal to 2ero f (x) = = x°-…

A: If we have a function f(ax) then the derivative of the function will be,     Here it is given that,

Q: 4. Find the second derivative for the following functions : a) y=(x+!)' (ans.:6x +6+ 12) x' b)…

A: (a)

Q: Find the first derivative of y with respect to x (y') of the given function using rules for…

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Q: 2. Find the derivative of the following functions. (a). g(x) = cos (2x + 1) (b)," f(x) = In (x² – 4)…

A: To find the derivative of the functions

Q: 4. Find the derivatives with respect to x of the function 2 – 3x^2. 5. Differentiate ax² + b to the…

A: Using derivative of composite function.

Q: Find the approximate value of derivative f(0) with the step size h for the following function by…

A: The three point end point formula with error is where h is the step size. If the step size is…

Q: Find the derivative of f(x) = In(e +4) 1 O 3e? e+4 3e3

A: We use the chain rule

Q: 2. Compute the second derivative using forward, backward, central difference and Taylor for the…

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Q: Let f(x) = ln x. By using the following formula for first derivative approximation: - - f'(x) ≈ f (x…

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Q: 2. Suppose that a model rocket blasts off, straight up, at time t = 0, with a vertical displacement…

A: If f(t) represent displacement of rocket  then f'(t) represent velocity and f''(t) represents…

Q: Find the second derivative of the function y=x(x² – 1) (А) 4x(5х2 - 3) в) 2x(5x2 - 6) (с) (2х -…

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Q: Givenf (x) = ln x, what is the derivative function f' (x), and what is its domain? f' (æ) = e², for…

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Q: What is the first derivative of f (x) = ln n A)? 3x²+7x 5х Select the correct answer below: бх-7 O…

A: Given query is to find the derivative of the expression.

Q: Solve for the derivative of the given functions using the Chain Rule formula. Suppose f(x) =…

A: Given: f(x)=(sin(2x)+1)7f'π2=?f'(π)=?(a)  f'(x)=?(b)  which is bigger in between f'(π2) and f'(π)

Q: For what values of x is the derivative of the function Vx2+ Vx equal to 1?

A: Given,           The derivative of x23+x3 equal to 1.

Q: ) f(t) = t2-2

A:

Q: x-2 For the function 10x) = ind f(X), the third denvative of t and i ), the fourth derivative ofT…

A: Please refer the attached image for complete solution.

Q: 4. Find the equation of the tangent line and the normal line to the graph of the given function at…

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Q: х+1 3.) y = х-2

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Q: 1) The derivative of f (x) = e2x² cos x is: 2) Simplifying the expression e n(4x-3) + eln 2x In(e3x)…

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Q: . Compute the central difference approximations of O (h^4) for the first derivative of y = cos(x) +…

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Q: The derivative of In x is and the derivative of a constant C is, sO X dx = In |x| +C for x> 0.

A: Given x>0, The differentation of natural log x is 1/x  And differentation of constant are zero.

Q: Let h be a function that has second derivative (x+ 1) (x – 2) (x + 4)e5 h"(x) Is x=2 the…

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Q: 1-Find the first derivative of the following function f( x) 5 cos (10x) + x' – 2x – 6x+ 10 For x=2…

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Q: Let f be the function defined for x > 0, with f (e) = 2 and f', the first derivative of f , given by…

A: Given, f be a function defined for x>0 and the derivative of f is f'x=x2lnx Point e, 2

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = In x²;…

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Q: Suppose that a model rocket blasts off, straight up, at time t = 0, with a vertical displacement…

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Q: Given the function below: Approximate the following using h = 0.2: f(x) = ex cos(x²) a. First…

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Q: 1. Find the derivative of each of the following functions a) f(x) = cos5x %3D b) g(x) = cos 5x c)…

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Q: 1. Find the anti-derivative of the following. e" (x + 1) dx x2

A: From the given information. Anti-derivative has to be calculated to the following expression.

Q: Find the derivative of the function f (x) = /e* – In(x) 12 – 1/x) O (ex12 – 1) O (e2 – 1/x) e? -x)

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Q: 2. Find the equation of the tangent line and normal line to the curve f(x)= 3x at the point(1,1). x²…

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Q: The second derivative of the function g is given by g' (x) = 0.1x³ – 0.29xª – 0.694x³ + 1.9136x². -…

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Q: f(x) = e*

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Q: Which of the following is the derivative of the function f (x) = 5x · e*? Of (x) = 5e* Of'(x) = 5e*…

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Q: Find the derivative of the function f(x) = Jet – In(/x) (e+12 – 1) O (e:/2 – 1/x)

A:

Q: 2. Given f(x) = x³ – 2x² + x + 2, find x e (-1, 3) such that f'(x) = 5. 3. Compute the derivative of…

A: Since you have posted multiple questions, as per our guidelines we are allowed to answer the first…

Q: Q3: find the derivative of In(x4+3x-1) a) f(x) = %3D x²+1 b) f(x) = 4x³ . log(x² + 2x) %3D c) f(x) =…

A: Use product rule of differentiation.

Q: What is the first derivative with respect to x of the function g(x) = 3/9x O 1/2 9.

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Q: The derivative of the function y = In (* + 1) (* - 1) is O y = O y = :- - 1 e+1 + -2 +1 ||

A: Question is solved.

Q: 2. Find the first derivative of the following expression: f(x) = (x2 + 1)sin a

A: take derivative  use the exponent rule

Q: 4) /() =2-2 3. 5) y = x*+2x+1 6.) f(x) =

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Q: Find a formula for n.th order derivative of the given functions. 1 b) f(x) = VT 1 a) f(x) = c) f(x)…

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Q: Find the second derivative f"(x) for f(x) = e(#+2)*.

A: First calculate the first derivative for f(x) using the chain rule.…

Q: Find the derivative of the given function. e5x (2x+1)5 f(x) = In Vx2+1

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Q: x² +2x+1 6.) f(x) = 3

A: Given :f(x)=x2+2x+13

Q: A. Give a piecewise-defined function f (x) with no extreme values. B. Find for x² – 4xy + y² = 7 by…

A: A). A piecewise function is: fx=2x≤1xx>1 Graph for this piecewise function is: B. Given function…

Q: 1- Find the first derivative of y with respect to x for the following functions: In5 7x y = log5 . a…

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Q: Compute the derivative of the given function. f (x) 10x-1/4 cos e + 7 sin a %3D -

A: