3. Determine the derivative of the function with respect to x. (Arrange your answer from highest degree to lowest degree) y = (x2 + 1)(x³ – x²)

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: Find derivatives of the function defined as follows. y = -4e-0.3x

A: Given,  y=−4e−0.3xFormula→ddxaex=aex  where a is constant.

Q: 1. If y = x³ + x - 5 then what is the derivative of y with respect to x?

A: Derivative of a function

Q: 1. Use limits to find the derivative of the following function at the point a = -1. 1 2x + 1 f(x)= =…

A: We have to find derivative

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

A:

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: 4. Determine the derivative of the function with respect to x. 8sin?(x² + 2) y = 4tan²(x² + 2)

A:

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: a. Determine the derivative of k(x) = (-2x* + 3x - 4)(x" – x- 1). Simplify your answer. b. What is…

A: The detailed solution is given below. Thank you

Q: Find the derivative of y with respect to x. + 1 5) y = sec-16x + -54 A) – 1 + (6x + 1)2 54 C) (6x +…

A:

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 of the following functions at an arbitrary point x: 8 a. f(x) = x3/2 b. f(x)…

A:

Q: 6. Determine the derivative of the following functions. Do not simplify. (a) y = 2t° +t+ e² 2 (b) y…

A: Given:           (a) y=2t5+t+e2Differentiating with respect to…

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: Use the alternative form of the derivative to find the derivative at x=c (If it exists)…

A: Given function is fx=x3+3x2+9. We know that, f'x=limx→cfx-fcx-c Given c=-3 Therefore,…

Q: a) Find an equation of the tangent line to the curve. y=f(x)3x2-4x at x = 2. b) Find the derivative…

A:

Q: 1. Using the definition of derivative, find the derivative of the following functions: 1 (a) y =xVx²…

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

Q: Let y=x+∣∣x2−8∣∣. Find the derivative of the function at x=3.

A: Given that y=x+x2-8.

Q: a) Find the derivative of g(x) = 3tanx – 4cotx. %3D b) What is the value of g 3.

A:

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

A:

Q: c) Use Leibnitz's Theorem to calculate the 4th derivative of y = x^sin (3x) d) Locate and identify…

A: We have to solve part c and d.

Q: 1. Find the derivative of the functions, do NOT simplify. a. y = In(8 – 3x) | b. y = ln /2.x + 1 3a2…

A: We have to pick the most challenging formula among differential formulas and solve it.

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: 2. Find the derivative of the following functions: (a). f(x) = x + 4x-2 + 6e" [1 Mark]

A:

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: 8. Evaluate the derivative of the function y with respect to x. y = 5*e*

A: This question is related to differentiation, We will solve it using given information.

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

A:

Q: 1. Apply the different rules for differentiation in finding the first derivative of the following…

A:

Q: 1 Find the derivative of g(x) = Vx-1 Find f'(x) and f"(x) of f(x) = 11x³.

A: Here we have to find the derivatives of the given function.

Q: (a) Use the definition of the derivative to calculate the first derivative f'(x) for the function…

A:

Q: Find the derivative of the given function at a given number 1. y=3x - 2 at f'(1) 2. y=x² -1 at f'(2)…

A: Find the derivatives at points. 1. y=3x2-2 for f'1. Apply derivative law: u±v' =u'±v'.…

Q: Find the derivative of y with respect to x. x7 x7 X' Inx- 98 y = 14

A:

Q: 1. Use the Power Rule and properties of derivatives to find the derivative of each function a) f(x)…

A: Here we have to find the derivative by using power rule and the properties of the derivative.

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: 11 8 Find the derivative of the function: y = 3(x – 4)' x-4

A:

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

A:

Q: Find the derivative y′(x) of the function that describes the general equation of a second order…

A:

Q: 4 Find the derivative of the function f(x) = %3D x +7 Provide your answer below: f'(x) =

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

Q: B) Find the Derivative by using the definition for the following 1-x function f(x) = 2x Then find…

A:

Q: Suppose the derivative of f exists, and assume that f(2) = 1, and f'(2) = 2. Let g(x) = x2f(x), and…

A: Apply the product rule to find the derivative of g(x) and then substitute the given values as…

Q: Let f(x) = 3x² + 2x − 10; a = 1. 1. Use the definition to find the derivative function f' 2. Find an…

A: The given function is: f(x)=3x2+2x-10

Q: Use the alternative form of the derivative to find the derivative of the function below at x = c (if…

A:

Q: 1. Suppose f(x)= 2x/x+2 (a)  Use the definition of derivative to find the slope of the tangent line…

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Q: II. Find the derivative of the following functions. 3. f(x) = x² cos(4x³)

A:

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. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: y=x4Inx

A: Topic = Derivative

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

A: