Compute ſ F · dr, where . dr,

Q: compute the derivative of f ◦ g. f (u) = eu, g(x) = x + x−1

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Q: Calculate f"(x), where f(x) = x cosx..

A: Given that, fx=xcosx

Q: Let f(x) = V5x + 4. Compute (f-1)'(2) using the Derivative of an Inverse Function Theorem.

A: Solution

Q: Find the derivative of f(w)=w78+2w.

A: dxndx= nxn-1---- Formula f(w) = w78 + 2w f'(w) = d(w78+2w)dw = 78 w77 + 2

Q: Find the first 3 iterates of the function f(z)=0.75z when 2o = 5. D 6.67, 8.89, 11.85 3.75, 2.8125,…

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Q: Compute the derivative of the following function. f(x) = 3x + 5x ex f'(x) = [ O

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Q: Compute the derivative of the given function. f(x) = 6x" + 3.9a6.7 + 76.7 Note: Use pi for T in your…

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Q: Consider a function f: R? → R°, the derivative of f isa O 3 x 3 matrix O 3 x 2 matrix O 2 x 3 matrix…

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Q: Find the 200th deriunte of f(x) = Xe X-

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Q: y=t In(\F)

A: We need to evaluate the derivative of the following function  y = t lnt

Q: Find F(s). F(s)

A: We use the table of Laplace transform to answer the given question.

Q: Use the Power Rule to compute the derivative.

A:

Q: Find the derivatives of the functions in Exercis

A: The rate of change in the value of the dependent variable with respect to the change in the value of…

Q: Compute f dx, where f(x)=|x|.

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Q: Differentiate the following function. r(t) = (4t,8/i,

A: We have to find derivative

Q: For f(x) = sinx, compute f ' at x = 0, π/6 , π/2 , 5π/6

A: Given, fx=sin x

Q: 1. Compute the derivative of the following function: F(x) = Jsin x

A: The function is  F(x)=∫sin xext2dt

Q: Find the derivative of f (w) = 7ln (w) + 18.

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Q: Find the derivative: j(x)=x3/a+(a/b)x2 -cx

A: Derivative formula:

Q: Use the Product Rule twice to find a formula for (fg)" in terms of f and g and their first and…

A: Product rule in derivative:  [A(x).B(x)]' = A(x).B'(x) + A'(x).B(x)

Q: Find the derivatives of the functions in Exercise

A: Given w=re-r

Q: F(X) = X on R did

A: I have proved the apsilon delta definition

Q: Find the derivative of the following function. 5 +x² -7 2 y= 9x 2 + 10x y' =O %3D

A:

Q: Calculate L3, R3, and M3 for the following function over the interval [0,3]. f(x) = Vx + 1

A: The given function f(x)=x+1 over the interval [0,3]

Q: Find the derivative of f(w) = √3w²

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Q: Find the derivative [ x ] dt O O O O

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Q: 17 3. f(a) = 2a3 11a %3D 8a2

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Q: Find the derivatives of the functions in Exercis

A: The given function is q=2r-r23.

Q: compute the derivative indicated. F(r, s, t) = r(s2 + t2), Frst

A: For a function in several variables partial derivative with respect to one variable is computed by…

Q: Differentiate the function y = Inx• In 13x. y' =O

A:

Q: Find the derivatives of the functions in Exercise

A: Explanation: Given that,  w=(2x-7)-1(x+5)     Formula used: According to the product rule of…

Q: Calculate the following derivative if f(x) = x*. f(4)(2) = %3D

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Q: Compute f dx, where f(x)= |x|

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Q: Differentiate. f(x) = In ( In (12x)) f'(x) =D %3D

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Q: Compute the derivative of the following function: f(x) = –6e3x +3

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Q: Find the derivative of f(t) = (In 6)*. f'(t)

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Q: Compute L(f(t)) for:

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Q: Suppose F(x,y)=where 0stsT. Find F.dr.

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Q: Find the first, second, third, and fourth derivative of the following function. f(z) = 725 + 7a-…

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Q: Find the derivative of the function C=25(11q^5−14)^8.

A: According to the differentiation rule the power comes down and reduces by one and then chain rule is…

Q: S læ), if |æ| < 1, 0, otherwise. (b) F{f(x)}, where f(x) =

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Q: Compute the derivative of f(x) = cot(4x).

A:

Q: Assume that we have functions f(x) and g(x) so that

A: Given functions - ∫-13f(x) dx = -1∫35f(x) dx = 4∫-11g(x) dx = 3∫15g(x) dx = 2∫-152f(x)-5g(x)dx = ?

Q: Find the derivative of f (w) = w5 +2w. %3D

A: The given function is as follows.

Q: Assume that f : (e)R is

A: Given, f:l→ℝ is a coordinate function for the straight line l and h : l→ℝ also any coordinate…

Q: Show that f xy = f yx for the following function: (x1² y) f(x, y) = 24 + In(x1² + y36 )

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Q: O Use implicit differentiation to find if x2 + xy + y? = 1.

A: solution:-

Q: Suppose that x = x(t) and y = y(t) are both functions of t. If 22 + y = 20, and -1 when x = 2 and y…

A: x2 + y2 = 20 Differentiate with respect to t 2x dx/dt + 2y dy/dt = 0 In this equation we put x = 2,…