Using the đết of derivative, fin rivative of f(x) = x² + 2x + 2.

Q: 13. f (x) = sinx3 (2х-1)2

A: I have stated the used formulas in the solution

Q: Using Leibnitz theorem, the nth derivative of xy, is

A: We have to find nth derivative of xy1 using Leibnitz theorem.

Q: According to the criterion of the first derivative, the image function has a point: f(x) = x2 + 10x…

A: The given function f(x)=x2+10x+21

Q: 1 Use the power rule to find the derivative of f(x) = Vx 15 f'(x) = %3D

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Q: y3D(i+sinx)(I-sinl)!

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Q: Use the limit definition of derivative to find the derivative of the function with respect to x.…

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Q: Compute the derivative using derivative rules that have been introduced so far. y = (x 4 + 5)3

A: Given equation is y=x4+53 Applying derivative with respect to x: dydx=dx4+53dx Using the power rule…

Q: Find the relative extrema of f(x) = 8+ 126x – 7x2 using both first and second derivative tests. f…

A: If second derivative is less than zero then there is relative maxima.

Q: Find the derivative of the function by the limit process. f(x) = 6/x

A: Given fx=6xddxfx=limh→0fx+h-fxh

Q: Estimate the second derivative of f (x) = difference approach with h=O.1? 25x3 6x2 + 7x -88 at x-2,…

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Q: 4. Find an equation of the tangent line to the curve, f(x) definition of the derivative. (Don't use…

A: Given problem:- Find an equation of the tangent line to the curve, f(x) = 1/(x2 + 1) by using the…

Q: Find all relative extrema of the function f(x) = x* – 4x2 + 2 by using the Second Derivative Test…

A: Given, The function  fx=x4-4x2+2 We have to find the all relative extrema of the function using the…

Q: Find all relative extrema of the function f(x) = x* – 4r +2 by using | the Second Derivative Test…

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Q: Compute the derivative using derivative rules that have been introduced so far y = √(9 +x + sinx)

A: We have to compute derivative of the function: y=9+x+sin x We know the formula of derivatives,…

Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 3 11. f(x) = x*,…

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Q: find the derivative of f(x) = (x²+4)(3x³ - 2x) at the point x = - 3[ use product rule] %3D B.

A: We have to find the derivative

Q: 3. Calculate the derivative of f (x) = x2 +1 showing all your work.

A: Using the formula u by v = vd/DX(u)-u d/DX(v)/v^2 According to the bartleby guidelines I can  solve…

Q: What is the derivative of f(x)=3cos(x)+2sin(x) at the point x=−π

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Q: On which derivative rule is the Substitution Rule based?

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Q: Fin derivative of the funclions. y=Log

A: The given function is: y=log3xx-12

Q: Use forward, backward and central difference to estimate the first derivative of f(x) = In(x) at x =…

A:

Q: What is the connection of the concept of limits to slope to derivatives (delta method to simple…

A: The limits of the function at a point are calculated using the formula . The limits are used to…

Q: Find the tangent line to the curve y = x^2 −5x + 11 at the point (1, 7). Use the limit definition of…

A: slope of the tangent line is m=dydx at (1,7)   By limit definition of…

Q: Compute the derivative using derivative rules that have been introduced so far y = ex-12

A: To differentiate y=ex-12, with respect to x, apply the exponential rule of differentiation,…

Q: 2. Determine the true error and relative true error when approximating the derivative of f (x) = -x²…

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Q: fcx)= Y文 メ ー^

A: Local extrema

Q: Find the relative extrema using first derivative test   f(x)=(x-2)^6

A: Consider the function f(x)=(x-2)^6

Q: 9) Use the second Derivative Test to find all relative extrema. f( x) = - (x + 2)°(x – 4)?

A: Find f'(x) and solve for x by putting f'(x)=0.

Q: 3. Find the derivative of f (x) tan (5x + 7), by first principle of differentiation

A: Given function is By first principle of differentiation, we have

Q: Consider Mean Value theorem for derivative for function f(x) 4(1-2x) in interval [0,1]. TCOS(TX) -

A:

Q: Compute the derivative using derivative rules that have been introduced so far       y = √(7x - 3)

A: To find the derivative: y=(7x-3) Solution: y=(7x-3) Differentiating both sides w.r.t x we get:…

Q: 1. f(x)=(2x-5) ¹ (4x+3)²

A: We need to find derivative.

Q: 4. Find an equation of the tangent line to the curve, f(x) = definition of the derivative. (Don't…

A: On solving this we will get

Q: find the derivative of f(x) = (x²+4)(3x³ – 2x) at the point x = - 3[ use product rule] В I !!

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Q: 3) Use the definition of derivative (do NOT use the short cut method) to find_ƒ'(x) given that f(x)…

A: This question is based on finding slope using definition of derivative.

Q: Find the derivative of the function f(x)=1/x using limit definition derivative

A: According to the given information it is required to calculate the derivative of the function using…

Q: Find the first derivative by applying the appropriate rules. DO NOT SIMPLIFY the algebra. (a) fx)…

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Q: Find the derivative of f(x)  =(a + 2x2) (x - x2) in twoways: by using the Product Rule and by…

A: We have given function  fx=a+2x2x-x2 At first we  will use product rule:…

Q: What is the rule for calculating the derivative of a composite of two differentiable functions? How…

A: Let us we consider a function which is real valued function which is composite of of two functions…

Q: Determine the second derivative of f (x)=x²e* at x =-2 with a step-size of h=0.50 using Central…

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Q: Find all relative extrema of the function f(x) = x² - 4x² + 2 by using the Second Derivative Test…

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Q: Use high-accuracy differentiation formula O(h) to estimate the first derivative of f(x)=log.x.…

A: Consider the given function, fx=logx Here we need to estimate the first derivative of the given…

Q: Find the derivative of the function at Po in the direction of A. f(xу) 3 - ху- Зу?, Po(-7,0),…

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Q: 4. Find the maxima/minima of f(x) = x³ – x using both 1st and 2nd derivative test.

A: Consider the function: fx=13x3-x. Find maxima, minima.   Find f'x by applying axn'=anxn-1.…

Q: Differentiate the functions showing the general process in determining the derivatives. Using the…

A: We need to differentiate given function.

Q: Find the derivative of f(x)= 11x^2 at x=1 please use definition of derivative formula

A: Given :   y = 11x2    at x =1

Q: Find the derivative of f(x) = 3/x at x = 3 by using the definition of derivative. Note that you will…

A: Given,f(x) = 3x at x = 3

Q: Obtain the first derivative of the function f (x) = sinx/x using Richardson's extrapolation with h =…

A: Given  f(x) = sinxx we have to obtained the first derivative of f(x) by using  Richardson's…

Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 3 11. f(x) = x*,…

A: Given :   f(x)=x4 , at x=3/2 f(x)=1/4 , at x=2