Give information on this application of derivatives:  Optimization

Q: Find the derivatives of all orders of the functions y = (4x2 + 3)(2 - x) x

A: We first expand the expression

Q: Use 1st and 2nd derivatives, sketch the graph of given function 2x x² - 1 f(x) =

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Q: Find the derivative of the function at the given point in the direction of A. Options are: 1)…

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Q: 5/- b. y =

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Q: %3D

A: Our Aim is to find the derivative of the following function given by:-g(x)=(x+x2) (x3+x+2) -(i)

Q: use the reciprocal rule or the quotient rule to determine the derivative of the function.…

A: Given :Bu=u2u+1To find the derivative of the above function using reciprocal rule or quotient rule.

Q: Find the derivative. 9 y = 4 .3 %3D

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Q: Find the derivative of y = 9" + 2.

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Q: 3 f(x) :

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Q: Find the derivatives of the functions in Exercise

A: The given function is y=x-35+π32

Q: State the derivative. Do not simplify. f(x) = e² - 22

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Q: give the derivatives examples with solution 2 examples of difference rule

A: Difference rule: ddxf-g=dfdx-dgdx

Q: Find derivative of y= x(3x-1)5

A: Use the product rule to differentiate the given function with respect to x…

Q: g(x) = x'n(x) %3D

A: We have to find derivative of given function-

Q: a) Using definition, compute the derivative function of f (x) = 4x7

A: Here, we will find derivative of given function by definition of derivative,

Q: Use differentials to give an informal justification for the chain rules for derivatives.

A: Consider the given statement. The chain rule of derivatives is defined as. dydx=dydududx Let's take…

Q: ソ= 5x-12 %3D

A: y=5x-12To find its derivative

Q: I need help with finding the derivative.  y=(2x^2   +   1)^2   (x-1)^3

A: Given: y=2x2+12x-13 We know that ddxu.v=vdudx+udvdx…

Q: Find the first and second derivatives of the function. (6t2 - 4)2 (5t2)

A: Given function: f(t) = (6t2 - 4)2 (5t2) = (36t4 - 48t2 + 16) (5t2) = 180t6 - 240t4 + 80t2 Recall the…

Q: Differentiate the function. y = etan(8) y' =

A: The given function is y=etanθ.

Q: Explain the rule of maximum and minimum using Derivatives with an example?

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Q: 2х — 1 f(x) = 1-2х

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Q: Calculate the derivative of the function y=(√3)2−5√2.

A: Given : the function is given as y=32-52 Now, we know that the derivation of constant function is…

Q: Find the derivatives using the four step rule: f(x) = 1-x2

A: Explanation of the answer is as follows

Q: Use the Chain Rule to find the derivative of the function. y (4x2 - 7)3 %3D

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Q: What do the derivatives of a function tell you about the shape of its graph?

A: If the first derivative is positive, then the graph increases. If the first derivative is negative,…

Q: Find the derivative of y=x2(x3-1)5

A: The given function is: y=x2x3-15

Q: The curve has a gradient function 2x - 3 and passes through (1,-6). Find the value of x when y = 0

A: Clear solution is given.

Q: How do I find the following derivatives?

A: Using 1 rules of log 2 derivatives of composite functions (chain rule)

Q: Find the derivative. 3/2 y%=

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Q: Derivatives

A: The given equation is y=ln tan-14x2-2the given problem is y is a function of x to find the…

Q: Make 2 examples (problem solving) regarding maximum and minimum values (application of derivatives.

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Q: 1 2 3. - 1

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Q: what are the real-life applications of derivatives?

A: Definition of derivatives helps to find real-life applications. Functions obtained after the…

Q: Please provide an example of real life computation and application of derivatives

A: Follow the steps.

Q: Can you please help me with derivatives and the power rule? I am struggling with that.

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Q: f(x)%3D (6- x²)3 — х? %3D

A: DIFFERENTIATION OR DERIVATIVE The differentiation is a process of finding the rate of change of one…

Q: Find the derivative. y = x-3 %3D %3D

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Q: 1/3 for

A: Answer

Q: y = Vz3 -4z-2 %3D

A: Given: y = z3 - 4z - 23   To find the derivatives.

Q: What information can be obtained from derivatives? Please provide 2 examples from the real world and…

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Q: -2x sinky sitlecex) -10

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Q: Differentiate the function by using the definition of derivatives. f(x + h) – f(x) f'(x) = lim h0…

A: Given: f(x)=x3

Q: Explain derivatives on optimization ?

A: Topic:- derivatives

Q: Find the derivative of y = x²( - %3D x2+1

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Q: find the derivative of y = (x + 1) (x² + 3).

A: Given          y=(x2+1)x3+3

Q: Differentiate the function by using the definition of derivatives. f(x + h) – f(x) f'(x) = lim h…

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Q: Find the derivative of the function y=x² + 3x - 1. Attach File

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Q: Sketch the graph of y= x2+2/x by using the properties of the derivative.

A: Given: y=x2+2x=x2+2x⇒y'=1-2x2⇒x2-2=0 ;  ⇒x=±2 are…

Q: What is the derivative of f(x) : %3D (* - (= – 17)' 1)*)*

A: The given function f(x) = x2-(x-1)32. We have to find derivative of f(x). To find derivative we use…