Let F (x) = (1 + t5)1/2 %3D dt. Then F'(x) =

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Q: Prove the formula.

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Q: Verify the homogeneity of the differential dy _ y²-2xy x2 - 2xy dx

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Q: Compute the indicated derivative using the chain rule. dy x = 5 + 3t, y = -8t; dx dy %3D dx

A: We have to find the indicated derivative by using chain rule: x=5+3t, y=-8t Differentiating first…

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A: To find ddx∫x3sin t dt We know that, ddx∫u(x)v(x)f(t) dt = f(v(x))v'(x)-f(u(x))u'(x) Then, we have,…

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Q: Find e-ax dx } first integrating and then transforming result.

A: Here we find Laplace transform

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Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

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Q: gin (t) et dt

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Q: ) Find: dx/dt  at  x=−4  if  y=−3x^2−2  and dy/dt=1. dx/dt=

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Q: Let xy = 3 and dy/dt = 4. Find dx/dt when x=2?

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A: follow next step

Q: Find the first-order partial derivative with respect to x of f(x,y) = e5x siny.

A: To find the first-order partial derivative with respect to x, given function, fx,y=e5x sin y

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A: Given:-y=5x2+3dxdt=2 at x=3To find : dydt

Q: Does the differential dy represent the change in f or the change inthe linear approximation to f ?…

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Q: Find dx dt dx dt at x 2 if y= = - 2x² - 1 and dy dt = - 3.

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A: Derivative, in mathematics the rate of change of a function with respect to a variable. Derivatives…

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Q: Find dy dy dt at x = z - 1 if y = -5x² + 3 and dx dt 5.

A: topic:- derivatives

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Q: Let y=sqrtX. Find dy/dt when x=4 and dx/dt=3

A: →Use chain rule of differentiation.→dxndx = n xn-1     When n = 12         dx12dx = 12 x12-1…

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A: Given,

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A: Topic = Derivative As per guidelines , at a time only one question can be answered. pleas repost for…

Q: Let x > 0 and b > 0. Show that

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Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.