Q: Find the limit, if it exists. V(t + 25)(t – 1)² lim 11t - 11 t-1+
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Q: Find the derivative of the function f(z) = (3x +1)In(4x+3) %3D and then evaluate it at x = 0. f' (0)…
A: Given : f(x)=(3x+1)ln(4x+3)
Q: Find the derivative of the function. 2 a) f(x) = x² ln(x) b) g(x) = 2" + log, (x + 5) +ez c) y =…
A: We have to find the derivative.
Q: The derivative of the function y = tan(In(vx² – 6x + 1)) is: 2 -
A: Chain Rule : (fg(x))' = f'(g(x)).g'(x). d(ax+b)ndx = n.a(ax+b)n-1 dtanxdx = sec2(x)
Q: Find the second derivative of the function y=x(x² – 1)² A) None of the given choices B) 2x(5x2 - 6)…
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Q: • Show that both of the functions f(x) = (x − 1)^4 and g(x) = x^3 −3x^2 + 3x+ 2 have stationary…
A: given functions fx=x-14gx=x3-3x2+3x+2 (A) to show both have stationary point at x=1 differentiate…
Q: 1 Find the derivative of f(x) = v2 – 3xª 2 -4 |
A: We use chain rule to find derivative
Q: Prove that for all a, b e R, the function f(x) = 3x - 4x³ + 6x² + ax + b has exactly one point where…
A: f'(x) is increasing function. But f'(x) is polynomial of degree 3. So it has exactly one real root…
Q: 3. Find the derivative. sh (a)l= - पक) (a) f(x) = x2 cos x +x tan r (b) h(x) = e" (x² + 4x) %3D t2…
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Q: In the function: f(x)= (3x^2)ln(x) , x>0 What are the inflection points of the function?
A: To find inflection points of the function we need second derivative of the function.Use product rule…
Q: Compute the derivatives at the given value of a g(x)=(3x-5)/(x-2) a=1
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Q: Let y= (x+sin(x))^5 Find g(x) and f(x) so that y= (f∘g)(x), and compute the derivative using the…
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Q: 4- Calculate the second derivative of the function y = f (x) defined by the equation x3 + y3 +3xy +…
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Q: Find the third Taylor's polynomial f(x) = x3 – x² + 3x + 1 which can easily find the derivative at…
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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If…
A: Differentiate the function fx=xx2+1 with respect to x, to obtain f'(x) and f''(x).…
Q: Given y = (ax? + bx )e -bx where a and b are constants. Find derivative of y with respect to x. e-bx…
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Q: Find the second, third, and fourth order derivatives of: y= f(x )= ax7 + bx3 + c y= f(x) = 3x/1-x…
A: It is simple derivative
Q: Find derivatives of the functions defined as follows: y =(3x3 - 4x)e-5x
A: Given: y=3x3-4xe-5x Let: y=f(x)=3x3-4xe-5x Product rule of differentiation is given by…
Q: 2. Find the equation of the secant line on the curve f(x) = -x² +2 passing through the points ro =…
A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…
Q: -e' 4. Y = e3x +e¬3X
A: Given: y=e3x-e-3xe3x+e-3x
Q: Use differentials and the graph of g′ to approximate (a)…
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Q: e3x-e-3x Y = e 3x+e-3x 4. t2 y= 72-1 5. X = t-1
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Q: 1 Find the derivative of the following function: f(x) = e2X(3x² - vx) 2e2X(6x - 1/x) O e'(6x -…
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Q: What is the derivative of the function f(x)= In(3x2) ? а. f'(x)= 2 b. None of these. с. 1 f'(x)= %3D…
A: We have given that The function is f(x) = ln(3x2)
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: The derivative of In x is and the derivative of a constant C is, sO X dx = In |x| +C for x> 0.
A: Given x>0, The differentation of natural log x is 1/x And differentation of constant are zero.
Q: Find the derivative of the function f(x) = – 2x1 + 5x – 7. A. -2x + 5 C. -2x? + 5 E. None of these…
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Q: Find the anti-derivative of the following: a.) f(x)=4x1/2-(4/x1/2) b.)…
A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…
Q: f. y=In(x8+1)
A: We will solve the problem
Q: Obtain the derivative of the function y y = (e*1) (In(2cos(x² – 4x))
A: The given function is: y=e3x+1ln2cosx2-4x
Q: Find the first derivative for the following function. g(x) = 4e3x*+2x %3D A. g'(x) = 4e3x*+2x +…
A: Given function: gx=4e3x5+2x Differentiate the above function w.r.t 'x' g'x=ddx4e3x5+2x
Q: The function g is differentiable, and the tangent line to the graph of y = g(x) at x = –2 is y = 2x…
A: Note that the slope of the line y=2x-2 is 2. Given that the tangent line to the graph of y=gx at…
Q: y = In (*+1) °(x+1), (x+2)3
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Q: h(x) = In (2x-2)+(x² +1)e³x-6 %D Calculate the derivative at x=2, that is h'(2)=
A: calculate the derivative as shown below: h'x=ddxln2x-2+x2+1e3x-6…
Q: 1 Let f(x)=- (3x – 5)² -6 and f'(x) = %3D (3x – 5) Find an equation of the line tangent to the graph…
A: The given function is: f(x)=1(3x-5)2
Q: 8) Find the derivatives of the following: a) f(x) = 4e* – 2x + 5 b) f(x) = ln 2x² c) f(x) = (4 – x)5
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Q: Q3: find the derivative of In(x4+3x-1) a) f(x) = %3D x²+1 b) f(x) = 4x³ . log(x² + 2x) %3D c) f(x) =…
A: Use product rule of differentiation.
Q: The derivative of the function y = In (* + 1) (* - 1) is O y = O y = :- - 1 e+1 + -2 +1 ||
A: Question is solved.
Q: Find the linearization of the function at a. 1. f(x) = x^4 + 3x^2, a = -1 2. f(x) = sin x, a =…
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Q: Find a linearization at a suitably chosen integer near a at which the given function and its…
A: To find a linearization at a suitable chosen integral near a= 0.11 at which the below function and…
Q: Suppose h(x) =23r +1 What is the correct result of the derivative of h with respect A h'(x) =3-23x +…
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Q: The derivative of the function y = (x² – 1)2 (x² + 2)³ is LA. 2x (x² +2)°(x² – 7) 2x (x² + 2) (x² +…
A: As we know that; The Power rule: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g' The chain rule:…
Q: Let y=(x+sin(x))^5 Find g(x) and f(x) so that y=(f∘g)(x), and compute the derivative using the…
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Q: Suppose 8 (x) = V x²+1, What is the correct result of the second derivative of g with respect to x?…
A: The function is given by gx = x2+1 To evaluate: The expression of g''x.
Q: Find the derivative of the given function e5x (2x+1)5 b. f(x) = In Vx²+1 f(x) = (x In x – x)
A: Given that: b. f(x)=lne5x(2x+1)5x2+1c. f(x)=(xlnx-x)
Q: 2. Find the derivative of (a) f(x) = x* + 3x 2+ 4e" 4 (b) f(x) = 2 tan(x)- 2"
A: Since you have asked multiple questions in a single request, we would be answering only the first…
Q: Find the derivatives of the following using chain rule. c. f(x)= lnx^2 +4e^x d. y=axe^bx e.…
A: Given: c. fx=lnx2+4ex d. y=axebx e. y=e3x3-x2+5x-6 To find : Derivatives using chain rule. Formulas…
Q: Find the derivative of the function y = In(x /x² + 14 X Vx²+14 1 Vx²+14 1 x²+14 x2+14
A: Topic:- derivatives Note:- as per our guideline if more than one question uploaded than only first…
Q: 2 Find the derivative of the following function f(x)=2x-10x -8 using the limiting process a.…
A: The function is given by f(x) = 2x2-10x - 8 To evaluate : The derivative of the function using…
Q: Find the derivative of the given function. e5x (2x+1)5 f(x) = In Vx2+1
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Let h(x)=f(x)g(x). If f(x)=2x2+1,g(1)=0, and g′(1)=−1, what is h′(1)?
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- Find the anti-derivative of the following: a.) f(x)=4x1/2-(4/x1/2) b.) f(x)=e2x+sin(4x)+2/x+1/(1-x2)1/2 c.) f(x)= 4x3+3x2+2x+1 d.) f(x)=sec(2x)tan(2x)Find the value a>0 such that the tangent line to the graph of f(x) = x^2(e^-7x) at x = a passes through the origin.The derivative of y = sin(e2x) is: 1. e2xcos(e2x) 2. 2cos(e2x) 3. 2e2xcos(e2x) 4. 2xcos(e2x)