31. Using one-sided derivatives, show that the function f(x) = {2. [x² +x, | 3х — 2, х> 1 does not have a derivative at x = 1.

Q: -What is the derivative of (x + 1)2 ? a) x? + 2 b) x c) x d) 2x+2

A: We will use chain rule of derivative

Q: 1) Find the derivative of the given function with respects to e 3tan ở In 3 y

A: Given

Q: Find the function with derivative f′(x)=e^3x that passes through the point P=(0,8/3) f(x)=

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Q: 2 a) For the function f(x) = X-3 , find f'(1) by using the definition of derivative.

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Q: 1. Find the derivative of f(x)= x(a+1), given a is a constant.

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Q: Determine the derivative of y (x) = ( 3 x² + 11 x + 4 )³ e-6 x with respect to x. y '(x) =

A: topic - derivative of a function

Q: 1. Determine the first derivative of the functions below with the rules for deriving the function:…

A: A Given function is y=4x3+32. Use formula ddxxn=nxn−1 Differentiate  y=4x3+32 by using the chain…

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: (14 Find the derivative of the function 7 (^ Y = x²+3 15 x²-3

A: Find the derivative of the function  y= [(x2+3)/(x2-3)]5

Q: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: c) If f'(x) =3+ 4x and the curve f(x) passes through the point (1, 8) i) Find f(x) ii) Find the…

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Q: -2 (a) Show that f'(x) using the definition of the derivative. (2x + 7)² (b) Find the equation of…

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Q: 10 Find the derivative f'(0) of f(x) = at x + 4 x = 0 using the laws of differentiation.

A: Derivative of the function

Q: 4- Calculate the second derivative of the function y = f (x) defined by the equation x3 + y3 +3xy +…

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Q: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In; x²+y

A: Given that a function f(x,y) is continuously differentiable on an open region, we can derive the…

Q: *(x) = x² +x – 7 , find f'(a) at a = -2 by using the definition of derivative.

A: To find the f'(a) using definition of derivative

Q: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In x² + y²

A: Given,            f(x, y)=3xy2+2xy+x2ln1x2+y2

Q: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

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Q: V². Find the derivative of f(x) = In x² +1 %3D x(2r - 1)2

A: Derivative: f(x)=lnx2+1x(2x3-1)2ln(mn)=ln m-ln nln(x2+1)=12ln(x2+1)

Q: 3. Find the derivative of y with respect to x in the following functions : 18x'y (ans.: (3x-2) a)…

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Q: 3- Show that this function is differentiable for all and find its derivative (2) = f(x+ jy) = x*-…

A: The necessary and sufficient condition for a complex function f(z)=U+iV  (where U,V are the real and…

Q: Зх + 7 Calculate the derivative of f(x) at x = 0. Give an exact answer in decimal form. 4х — 5 f'(0)…

A: *The given function f(x) is, f(x)=3x+74x-5 Apply quotient rule on the above function to get the…

Q: Use forward-difference formula to evaluate the first derivative of y=x3−4y=x3−4 at x=0x=0 using a…

A: Given function is  y=x3−4. We have to evaluate the first derivative of y=x3−4 at x=0 using a value…

Q: 4- Calculate the second derivative of the function y = f(x) defined by the equation x³ + y3 +3xy +…

A: The given function is: x3+y3+3xy+3y2+6x+6y=0

Q: Q. / Find the derivative of y = (In(x²))'n(x²).

A:

Q: 11. Use the limit definition to find the derivative of f(x) = x² -2 x. 12. Find an equation of the…

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Q: 3- Show that this function is differentiable for all and find its derivative f(2) = f(x+jy) x - 15x…

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Q: 1 6. Find the derivative of f(x)= 1 at the point 8, Vx+1

A: Given

Q: 4. Find the second derivative for the following function a) )* 22 y3(x+ (an b) f(x)=/2x + at x= 2 c)…

A: See the attachment

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: 2.) f(x) = (x5 – 2x³ + 1) 3

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Q: What is the value of y' at x=-4 is ______? Evaluate the derivatives of the given function for the…

A: The function is given by y = 5x2-x+53-3x-x2 To evaluate : The value of y' at x =-4

Q: 5х f(x) = 2) Find the first derivative given that J2x+3

A: Solved below...

Q: #4) Given the function f (x) =x³-x² +2x- 1. Use the second derivative test, where applicable, to…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 7. Consider the function f(x) X - 3 a. Using the definition of the derivative at a point, calculate…

A: Given : f(x) = x / x - 3   (1) f' (2)  (2) tangent line when x = 2 (3) normal line when x = 2

Q: 4) Find the following derivatives using derivative rules, not the definition. a) f(x) =x -3F+5

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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: 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: 1. Use the definition of derivative to find f'(1) 2r2 b) f(x) = Vx

A: Derivative of the function using definition

Q: 10. Find the particular antiderivative of the derivative f'(x) = 3x-1 – x-2 where f(1) = 5.

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Q: IV. Obtain the 2nd Derivative of the given function. 7. 4y – xy? 1

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Q: 1. Find the derivative of f(x) = e" (x² – 1)ª. Make any obvious simplifications.

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

A: take derivative  use the exponent rule

Q: 6.) Find the derivative of the fonction 2 8- g'cx) =

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Q: 10 The derivative of the function f(x) = x7 + - 10 726 + (r³) 10 71° + (2) 1 10 7x + 10 10 726 (z²)…

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Q: x² +2x+1 6.) f(x) = 3

A: The given function is f(x)=x2+2x+13. Find the first derivative or f'x of the functions by using the…

Q: Find the derivative of the function f(x) = 3x? – - 12x – 28 by definition of derivatives f(x + h) –…

A: A function is a relation which maps each value in its domain to exactly one value in its range. The…

Q: 1.) f(x) = (2x + 1)(3x – 2)

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Q: 2. Consider the function f(x) = e¯*. -2x (a) Show that the derivative is f'(x) = %3D

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