Suppose that f(1) = 3, f(4) = 5, f '(1) = 4, f '(4) = 4, and f " is continuous. Find the value of xf "(x) dx.

Q: Find the derivative of the function. 1 In(1 + 49x 14 y = x arctan 7x dy

A: Given y = xtan-1(7x) -114ln(1+49x2)dydx = d xtan-1(7x) -114ln(1+49x2)dxdydx =…

Q: Solve the first derivative of f(x) = e-2x In x at x 0.5 using forward finite-divided difference and…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the derivative of y with respect to x. y = In (tan 1(5x)) dy dx

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Q: In xy = x² + sin xy

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Q: Find the derivative of y 16 In (In(6x)). (Use symbolic notation and fractions where needed.) dy dx…

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Q: Find the derivative of the function. rsin(x) y = In(1 + 5v) dv y'(x) = sin x In(1+5 cos x) + cos x…

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Q: Find dx 2 using implicit differentiation: In x + In y + e tan x = 0

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Q: Find the derivative of the y with respect to x. Y=on (13x)+x dy/dx

A: Given  Y=13x+xdydx To find derivative of y with respect to x

Q: Determine the anti-derivative of Y = 2e3x +5 and use the fact that y(0) = 7 to %3D dx determine c,…

A: We first separate the variables and then integrate  c= integrating constant Formula used:

Q: ,2x Calculate the second derivatives of function f(x) = sin(x) + Ide²x at point x = 0.625 using…

A: Three point central differential formula for 2nd derivative   f′′(x)= f(x-h)-2f(x)+f(x+h)h2 Five…

Q: Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f…

A: We will prove the given statement.

Q: If sin(5x - 5y + z) = 0, use implicit differentiation to find the first partial derivatives with…

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Q: Can you help me with this problem step by step?

A: To determine the derivative of given function.

Q: If f(x, y) = ln(x + y), then total derivative or total differential of f at x = 3 and y = 20 is : Y

A: Given data: The given expression for the function is f(x,y)=ln(x+y). The given value of x is x=3.…

Q: Find the derivative of f (x) = Ln e*+1 using the limit process. %3D

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Q: sin x (cos x+1) dx 7. S (cosx +1)2

A: Given that: ∫sinx(cosx+1)(cosx+1)2dx           NOTE: As per our answering guidelines, we can only…

Q: Find the general anti-derivative of f(x) = + Vx on a continuous interval.

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Q: Compute the higher derivative.

A: Given, d3dx3sin 2x

Q: Find the derivative of y with respect to x if y=∫0ln(3x) sin(6et )dt

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Q: Find one anti derivative of (x+1)^2 and then find  integral(x+1)^2 dx.

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Q: Find the derivative of the function y = 4x + In(x + 4). dy dx

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Q: 6. Differentiate: a. f(x) In (In (3x)) b. Find equation of the tangent line to the graph of y-e³x.…

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Q: The derivative of: y =0( sin (In (0))) in (In (0))) + cos(ln (0)) is is:

A: Given function is rewriting in other variables as: y=x(sin(ln(x)))+cos(ln(x)) Product rule of…

Q: Find dy/dx by implicit differentiation. x²y³ -yax dy/dx =

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Q: What is the derivative of * In(xy) = e"y – arccos(xy)?

A: We differentiate given equation

Q: Find the derivative of y with respect to X. y = tan 1 5x 105x(1 + 5x) 2(1 + 5x/5x J1- 5x 1+ 5x

A: It is derivative.

Q: Compute the derivative of h(sinx) at x = π,/6 , assuming that h' (0.5) = 10.

A: We have to compute the derivative of function hsin x at x=π6, assuming that h'0.5=10. We know the…

Q: Find the indic ed derivative. dz x2 for z = x2 dx 1 - x - 2x2 dz dx

A: Formulas:

Q: Find the Indicated Derivative dy 1. y = x5 - 3x* + 2x3 - 2x2 + 7x - 1, dx dy 2. y =x2+x-3 + 3, dx…

A: Given:- y = x5 -3x4 +2x3 -2x2 +7x-1 y =0.5x-2 + (2x-3/3) +3 To find:- dy/dx

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: = Determine the equation of the tangent line to the graph of f(x) = I x+ln x cosh (√2t - 1) dt at x…

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Q: Consider f(x) = 3 − cosx on the interval [0, 7]. When will the first derivative equal zero?

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Q: Find the derivative of F(x) = 4 n sin(t) dt. %3D dx 3x² cos(x)

A: Integral calculus is one of the two main parts of calculus that is concerned with the study of…

Q: Compute the equation of the tangent line to f (x) = sin(Tx) at x=0.5.

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Q: Give the derivative of f(x) arctan an(e³*) at the point where x = 0.

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Q: 9. For f(x) = arctan (2 sin ( Vx )) , compute the first derivative at the point %3D X =

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Q: Find the derivative of the function. "sin(x) In(7 + 9v) dv /cos(x) y'(x) =

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Q: 1 m' (x) = x In(x)

A: Given: m'x=1xlnx for finding anti-derivative of given expression, we substitute lnx=u…

Q: derivative of a Y with respect to x Y= ln (15x)+3x dy/dx=

A: Use formula of derivative to solve

Q: Find the derivative of the function. sin(x) y = /cos(x) In(8 + 3v) dv y'(x) = 0

A: Here we use Leibniz integral rule and define the formula:

Q: If fex, yJ-o find dy /af partial derivative off dx

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Q: Find the derivative of y(x) = In (7(In(x))* ). %3D (Use symbolic notation and fractions where…

A: Topic = Derivative

Q: Find the derivative of F(x) = n sin(t) dt. 3x2 d dx cos(x)

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Q: Find the derivative. 3t cos (t) dt %3D O 3x cos (x4) O &va cos (x4) O 3 cos (x4) - 3x sin (x4) O cos…

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Q: Can you help me with this problem step by step?

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Q: Compute the second derivative with respect to r of 3x + 8 y = at x = 1.

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Q: Find the derivative of y with respect to x. 1 y = In x/x+5 dy dx II

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

A: Solution is given below:

Q: Find the 1st and 2nd derivative of: Vx + Jy = va

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