For what value of the constant c is the function f continuous on (-, 0)? S cx2 + 5x x3 – cx if x < 4 f(x) = %3D if x > 4

Q: Show that is C is a function of x with derivative C'=C/x and N=C/x, the d/dx (C/x)=(C'-B)/x

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Q: Q1) The dervative of the function f(x)= |x+2, using the definition of derivative is 1 b)- a) x+2 x+2

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Q: Which function has the same derivative function f (x) as g(x) = Inx + x? – x? Select one: O a. f(x)…

A: Given function is : gx=lnx+x2-x

Q: The derivative of the function y= (z+7x)5 is O 5(2 + 72) (3z?+7) O 5(7 +7x) (3x² + 7) O 5(r +7x)*(3²…

A: Topic- derivative

Q: Compute the first and second derivatives of (x+4)e^x. Give the intervals wherethe function isa)…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Use the second derivative test to find the extreme values of the function J () = x³ – su² 24X .

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Q: Use the clerivative rules to tind the deriVative of y. y=(x² + y> x²? (x-1)s y= (4x-1)3 2x+)

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Q: Find the derivative of the function. f(x) = (x³ + s ]Inx O a. x*(1+Inx)+5 O b. x'(1+31nx)+ 5 O c…

A: We have to check

Q: Find the derivative of the function. f(x) = In(x + V7 + x²) f '(x) =

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Q: The fifth derivative of the function f(x) = 5x° is a constar False O True

A: Given query is to find statement is true or false.

Q: Which among the choices has the first derivative that is e (2x+1) (x +3) ? Of(띠) 3D + 글z2 + 2x-8 O…

A: given function has first derivative is f'x=2x+1x+3    f'x    =2x2+7x+3

Q: The derivative of y= xh* is O 1) (In x)(xh*-) O 2) 2 an x)(xh*) O 3) (In x)* O 4) xhx

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Q: Find the indicated derivative dz/do for z= x^3+x^2/1-x-4x^2

A: We have to find derivative

Q: what is the derivative of y=e^-1/2x(C1cos3x+C2sin3x) and evaluate if x=0, y'=8

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Q: if f'f′ is the derivativeof ff with 2∫1f'(x)dx=10∫12f′(x)dx=10 and f(2)=4,f(2)=4, then f(1)

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Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

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Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

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Q: Find the linearizationsof the following functions at x = 0. ex

A: fx=ex at x=0. Now differentiating with respect to x, we get f/x=dexdx=ex Now, f0=e0=1 &amp; f/0=e0=1

Q: Find the derivative of the below functions: In(x) y = 1-8 In (x) y' = (a) = In(/ 5x – 7) y = INV5X -…

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Q: What is the derivative of the function f(x) = e^(2x-3) for x=2 using the back difference method with…

A: Backward difference  First derivative :   when error O(h) . First derivative :   when error .

Q: dy Find for the following function: dx 1- y = etan'x 2- x³y + x²y = 2 at x = 2 3- y = log4(x³ – x)

A: Finding Derivatives by applying chain rule of derivative

Q: Jaimie, a MAT student, claims that "For a continuous function f(x), defined on an interval [a ,b],…

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Q: What is the 4th derivative at x = 0 of the function f(z) = (2r + 1)* %3D

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Q: If f(x) is a differentiable function such that f(6) = f'(6) = 2, compute the following derivative. d…

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Q: find the most general anti derivative  f(x) = e^2

A: A function F(x) is called an antiderivative of f(x) if F’(x) = f(x).   The function f(x) is the…

Q: Find dy/dx for f(x)=(Inx)x^2

A: Given:y=fx=lnxx2We need to find: dydx

Q: Find the derivative: n[(x³ + 2) (x² + 3)]. Evaluate S dx. Зx8 — 2 2x*- x2 Evaluate dx.

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Q: Find the actual error when the first derivative of f (x) = In x at x = 2 is approximated by the…

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Q: Which function has the same derivative function f(x) as g(x) = lnx + x² – x? Select one: O a. f(x) =…

A: Given: g(x)=ln x+x2-x The derivative of ln x is 1x. The rule for differentiation is ddxxn=nxn-1…

Q: use the definiton of a derivative to find the deriviative of f(x)=3x^2+x

A: we have to determine the derivative of f(x) using definition  of derivative .f(x) is given as below

Q: dy Find by implicit differentiation. 1. x - xy +y = 7 2. x'y +yx = -3

A: 1. Given relation is, x3-xy+y2=7 Differentiating these with respect to x we get,…

Q: Find A and B given that the derivative of Ax? + B, x –1 is everywhere continuous.

A: Given function is f(x)=Ax2+B,x&lt;-1Bx5+Ax+4,x≥-1 We have to find the value of A and B  so that the…

Q: Use the Quotient Rule to show that the Powers of x Rule appies to negative Integer powers. That s,…

A: The given function is fx=1xk   where k&gt;0. Quotient rule says that ddxfg=gdfdx-fdgdxg2.

Q: F(x)=In(52x+n • (x+2) ) %3D

A: Find the derivative of the function

Q: What is the anti-derivative of q(x) = 2e+5 3x 3 ? (Do not include the constant C in your answer.)

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Q: 二D f(x) Vx3 x3+6x²

A: Given fx=x3+6x2 Rewriting the equation: fx=x3+6x212

Q: 4. Show in two ways that the function f(z) = exp(z²2) is entire. What is its derivative? Ans. f'(z)…

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Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

Q: Evaluate dy for f(x)= (square root of x) +3 where x=9 and dx=0.12

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Q: In the interval 3 < x < 4 of the first derivative test, f(x) is a. Not moving b. Changes direction…

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Q: If f(x) = S dt for x 2 1, find f'(2). 1+lnt

A: Simply use the formula for the derivative of an antiderivative.

Q: Q1) The dervative of the function f(x)= |x+2 using the definition of derivative is

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Q: If f (x) = In (4a + 1), then its third derivative is f(3) (æ) = %3D

A: In this question, concept of derivative is applied. Derivative The derivative expresses the rate of…

Q: Evaluate the second derivative of e22.1.png ... acos(byx) f(x) x2 if a = 165 and b = 0.3 at x = 3…

A: Follow step 2nd and 3rd.

Q: Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=4f(0)=4 and…

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Q: Evaluate the second derivative of e22.1.png acos(b/x) f(x) = x2 if a = 149 and b = 0.3 at x = 3…

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Q: Find the particular antiderivative of the following derivative that satisfies the C'(x) = 5x2 – 6x;…

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Q: 8.) f(x) = v5x6 – 12 10.) f(x) = (x - 4x- 7)

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Q: - Integrate the following function: -3 2x+3 dx y = Jo x²+3x-5

A: The given integral is: y=∫032x+3x2+3x-5dx To evaluate this integral, consider x2+3x-5=t   .....(1)…

Q: Find for the following function: dx 4- y = In2 5- tan-1 V4x - 5

A: Topic : differentiation