In the following, the dot notation is used to indicate the time derivative of a function, i.e. ƒ = at 1. Consider the following multi-variable function, f(x,x,t) = 20xx + x³t + 5x +i Calculate the following: a. af /ðt b. af /əx c. ôf /ax d d. dt

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A: We will find the derivative of the function f(t) as following.

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A: Consider the first function: ft=2t2+5t+13t-4 Differentiate ft with respect to t:…

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A: Given  fx,y = -3x2+4y3+2xe32y

Q: In the following, the dot notation is used to indicate the time derivative of a function, i.e. f %3D…

A: Given- Consider the following multi-variable function, fx, x˙, t = 20xx˙ + x3t + 5x + x˙ To find-…

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A: Explanation of the answer is as follows

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A: The formula for the backward difference is f'x=fxi+1-fxih Now, h=0.1xi=2xi+1=xi+h=2+0.1=2.1fx=x2ex

Q: Find the derivative of function defined as follows.

A: Given: fx=82x2+5 Differentiating the given function fx with respect to x, f'x=ddx82x2+5…

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Q: Q5:- Find the first order derivative of each of the following functions: c) ysecx = x(secy) %3D

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Q: V. Find the third derivative q = tsecv0.2t" +1 Where r is the last digit of your university ID.

A: It is given that: qt=tsec0.2t4+1 Let u=0.2t4+1 qt=tsecu Differentiate w.r.t t to get:…

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A:

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A: we have to find the derivative of the irrational function y=mxn

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A:

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A: Given  S(t)=t2-t To find the derivative using first principle at t=1/2

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A: Given : y = xcos-1x+1-2x

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A:

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A:

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A:

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A: We will find f'(x) using the product rule and the chain rule.

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A:

Q: I. Find the derivative of the given function by definition f (s) = (5s" + 2)(2s" – 1) Where r is the…

A: Function:                          f(s)=(5sr+2)(2sr-1)   Here :                           r=4;

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A: Given : gt = t4+4t4-4

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Q: Find derivative of the 6tanx following function d d.x

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Q: d'y of y = r10 sec 2

A: y = x10 - sec x Differentiating with respect to "x" dxdy = 10x9 - sec x tan x Again, Differentiating…

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Q: Use the Quotient Rule to find the derivative of the function.                                f(t) =…

A: the quotient rule of the derivative states dydt=v.dudt-u.dvdtv2 here v=t3,u=cost we will derivate it…

Q: 6. v(y) = In (y² – 8y – 1)

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