1 2. Let F(x) = | dt 1+ (In t)² Find the derivative F'(r). Simplify your answer.

Q: Find the derivative of h(x) = | 14 arctan(t) dt. h'(x) = ||

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Q: 2. Compute the derivative of the following functions: 1-e-* (a) f(x) = V1 – sin³ x, (b) f(x) =

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Q: 4. Find the derivative of the function f(x) = (sin x)c0s ". COS x

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Q: 4. It f(x,)= (x?+Zy^)+Z and ū= a.) Find the derivative of t in the direction Of ū at 13,2) -

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Q: 5. Why does it make graphical sense that the derivative of aconstant is zero? That the derivative of…

A: Derivative of a function is a slope of function on given point, or derivative is a rate of change of…

Q: 9 tan t Find the derivative of the function y = 2 + 2 sect dy dt

A: Explanation and solutions is given below....

Q: 5. Find the derivative of: a. f(x) = cos(e³x-4)

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Q: F(x) = f Cos t dt

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Q: Find the derivative of the function #1) F(x) = In(2x+3)· (4x +7) tan(x) t +4 dt t2 +2 # 2) h(x)= |

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Q: 7. Compute the derivative of y = tan-(Kr) 1. at the point r = K

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Q: 2. Calculate the derivative of the following. А. y = (x* – 3x² + 5x) ³ DUKAS B. y = tan²(x² + 5x –…

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Q: 12. Find derivative of the following composite function using the Chain Rule: 2y t(y) = 6y² + 1+y?…

A: We have to find derivative

Q: cosh r – 1 · (xª4 + 2) +2). Compute the derivative of y = In | (2x + 1)

A: Given problem:-

Q: 1. f(x) =In (ta n"x)

A: Given query is to find the first derivative of the expression.

Q: What is the derivative of (6 x+1)5 (4 x-21)16 (21 x-23)3 (3 x+25)4 y = In with respect to x?…

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Q: 1) Find the derivative of the function 2 + X y = arctan V 2 – x .Simplify where possible.

A: Answer and explanation is given below..

Q: (3) Compute the derivative of the function e2t cos tdt.

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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: Find the derivative of the function tanh-e* A. -1/2 csch x B. 1/2 csch x C. -1/2 csch 2x D. -1/2…

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Q: 2. Find the derivative of: (a) A(x) = [ 1n | In(sin(3t)) dt (b) A(x) = L, In(sin(3t)) dt

A: According to the Leibinitz rule :

Q: _6. What is the derivative of f(x) = (5 – x²)²? а. 2(5- х2) b. 10 – 2x2 C. 4x3 – 20x d.(5 - x?)(5 -…

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Q: 23.3 Use centered difference approximations to estimate the first and second derivatives of y = e*…

A: The formula for the first derivative of a function fx at x=a by centered difference approximation is…

Q: What is the first derivative of the expression (xy)^x = e? Hint: this involves implicit…

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Q: (3e)® arctan (3x³) In(e2«) arccos(5x) 1. Find the derivative of f (x)

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Q: 2. Find the derivative of the function. y = e* In (sinæ)

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Q: (§5.5, Q34) Calculate the derivative d dæ ), Vi dt.

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Q: 9. Find the derivative of the function using chain rule. f(t) = 3t In t

A: To find the derivative of the function

Q: 3. Calculate the derivative of f(x) = tan(4t) dt. %3D -1/16

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Q: 2. Prove from the definition of derivative that for n EZ, d ng"-1 dr

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Q: 4. Find the derivative of the functions. (2x2-3) a. y = (x247)5 sin x b. y = 1+cosx

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Q: 2. Approximate the derivative of f(x) forward, backward, and central difference method and step size…

A: To obtain the derivative at the point x0,y0, the following methods can be used:- The forward…

Q: Find the derivative of F(x)

A: To Determine: find the derivative of F(x) Given: we have Fx=∫2x3costdt Explanation: we have a…

Q: (2) Find the derivative of the following: y = xsinx + x² y = (x² + 1)** + sin(x*)+ x* 2. 3. Iny = e'…

A: Since you have asked a question with multiple subparts, we will solve the first three subparts for…

Q: How do you solve question 10?

A: Given function is  By definition of derivative , we have

Q: 19 f(2) = | t² dt then f'(x) = If Find the derivative of g(x) = sin(t') dt. g'(x) =

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Q: Can you help me step by step?

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Q: In x 3. Compute the approximate derivative of f(x) = · at x = 2, using three-midpoint x² + 1 formula…

A: Given is a function and at a point at which the approximate value of first derivative of the…

Q: 3. Find the derivative of f(x, y, z) = z2 + ye" at (In 2, 2, 1/2) in the direction in which the…

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Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: 3. F(x) = " In(x) (4t + et) dt. Find the derivative of F(x).

A: Given, F(x)=∫1ln(x)(4t+et)dt To find : Derivative of F(x) By using the second fundamental theorem of…

Q: -7/2 = 8. Calculate the derivative of y with respect to , if x/2 + y dy dx

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Q: 15 - What is the approximate derivative of f(x) = 5x³ + 4x² if we use f(ze+h)–f(za) forward…

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Q: (4)The instantaneous rate of change of f(r) = e- at a = 1 is . .. (5) The derivative of f(x) = sec2…

A: (4) We have So we get the instantaneous rate of change of the function at  as .

Q: 2 e -8; x(0) = 1 dt

A: Solution is given below:

Q: Determine the derivative of the function (x) = %3D 3+e3*

A: Authoring guidelines:…

Q: et dt. · e2t 5. Find and simplify the derivative of f(x) = %3D 1 -2 In z

A: Assume g'(t) = e^t/(1-e^(2t))

Q: Calculate the derivative of the function g(x)=x∫√x(t2−t)dt at x=1.

A: using the fundamental theorem of calculus we find g'(x)

Q: Find the derivative of the function. (x-7)(x²+2x) +3 y = O A. OB. dy dx O D. dy dx dy O C. dx dy dx…

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