=: (1)6 In(t)dt, 1, = e.

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A: Given ddx∫x5e7xlntdt.

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A: We will use the formula: ddx∫abf(t)dt=f(b)dbdx-f(a)dadx Note, here a and b both are functions of x.…

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Q: 5. Use the properties of differential operators to solve for the product of (D+x²)(xD + 2)y

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Q: Calculate the derivative 10z d dz In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

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A: To use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.y=∫sin…

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A: [Fundamental theorem of calculus ddx∫g(x)h(x)f(t)dt=f(h(x))*h'(x)-f(g(x))*g'(x) ]…

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Q: Use Part 1 of the Fundamental Theorem of Calculus tofind the derivative of the function.

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Q: 1. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative, g'(x), of the function.…

A: solnThe FTOC tell us that:ddx∫0xf(f)dt=f(x)  for any constant a(a) g(x)=∫2xt3  sin  2tdt…

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A: As per guidelines we can solve three subparts at a time, so the first three subparts can be solved…

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A: The Fundamental Theorem of Calculus says: F(x)=∫ag(x)f(t) dt⇒F'(x)=f(g(x))g'(x)

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Q: A derivative in Leibniz notation is written as a fraction of differentials. A True B) False

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

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Q: Calculate the derivative a s In (t)dt using Part 2 of the Fundamental Theorem of Calculus. Enclose…

A: ddx∫x8e5x ln(t) dt  Proof:    ddx ∫x8e5x ln(t) =ln (e5x) ddx( e5x ) - ln (x8) ddx( x8)…

Q: 11a d dz In (t)dt

A: To find: ddx∫x4e11xlntdt

Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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Q: Let f(x, y,z) = z-sin(xy), x = t, y = In t, z = e4. Find derivative of f directly and by using chain…

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Q: 2) Find second derivative d'F/dt? of 312-2 F? = 13 and find it at (t,F) = (-1,2)

A: We have to find the required second derivative at the given point.

Q: lve (D² –1) y =(x³ +2x² +x+6)e²* using differential operators method.

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Q: Calculate the derivative 26 dt d (6£4 dx using Part 2 of the Fundamental Theorem of Calculus. 26 dt…

A: According to the fundamental theorem o calculus:

Q: Use fundamental theorem of calculus .4 –dx x In x 2,

A: Follow the steps.