z = eY/x + 2 log(2x²y)

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y * logy x *

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Q: Consider f (x, y) = log(r² + y²) f.(x, y) = %3D and fy(1,0) = %3D

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Q: That the value of the integration g(1) = 0, g(2) = 0 1-e) -dt where g is a function that is…

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Q: X* Q: Prove that the function y- 2 2 x+1+/log Vx+Jx +1 + log satisfies the relationship 2y=x dx

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Q: Find the MacLaurin polynomial of degree 7 for the function sin (ot) dt. F(X) = %3D

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Q: find the absolute extrema of thefunction on the closed interval. y=x^{2}-8 \ln x,[1,5]

A: Given:- function y=x2-8 Inxdefined on the interval 1, 5 The derivative of the function is y'=2x-8x…

Q: Let y = tan find the differential dy of the function.

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Q: 1 dx = +C (x+1)² X+1

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Q: Let y = f(x), where f(x) = 7x³ + 3x. Find the differential of the function. dy = X

A: The differential of y is the derivative of the function times the differential of x,

Q: Let f(x, y) = y log (xy). Find: (г, у) fyr (x, y)

A: We have to find the partial differential fyy and fyx.

Q: Find the linear approximation of f(x) = ln x at 1 and use it to estimate ln(1.33). L(x) In(1.33) =

A: Given : fx = lnx

Q: 17. Consider f(x) = dt. DO NOT state that f(x) = In x but explain how it behaves exactly like the…

A: In the question we need to evaluate the integral.

Q: f(x, y) = 1/(xy), then the marginal pdf of X is (log x)/y. Is this statement True/False?

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Q: 23: Find The Domain of the Function. y = sin (log, x²]

A: Given: y=sin-1[log4x2]

Q: (c) Use implicit differentiation to compute dy/dx: In(xy) = x°y² + e"

A: We have to find the dydx.

Q: Use the Beta and gamma function -1 n! 1- Prove that x™(ln x)"dx (m+1)n+1

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y logy x * * -

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Q: Recall the chain rule from differential calculus: f (g (æ)) = f' (9 (æ)) · g' (æ). d dx Find de tan…

A: We have to find

Q: Eliminate the arbitrary constants a. x = -In t, y = at + bt?

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Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate ln(1.34). L(x) =…

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Q: If e (3x + 2)e2* dy 3 4 using logarithmic differentiation. (b) show that +2 2.x-1 %3D (2x-1) dx 3x…

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Q: Let y = (r-15x)m(). Find dy using the method of logarithmic d.x differentiation. Express your answer…

A: We will solve the problem

Q: Let y = f(x), where f(x) = x4 − 5x. Find the differential of the function.

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y * logy x |

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Q: az dz +y =5 ax If z= log ( x+x*y+y° ), Prove that x

A: We can prove this using the rules of partial derivative

Q: Let f(x) /1+ In (t) dt. 2 f(e) = D

A: Differentiate wrt x

Q: Determine dydx of function g 1 g(x, y) = cos (Tx/T) + log3 (x – y) |

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Q: Let y = (x° – 15a)m(@). Find dy using the method of logarithmic dx differentiation. Express your…

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Q: Q4/ Use Logarithmic Differentiation to find dy/dx for the following functions: 1. y = V(x2 + 1)(x –…

A: Differentiation of ln(ax+b) = a/(ax+b)

Q: If f(x) = S dt for x 2 1, find f'(2). 1+lnt

A: Simply use the formula for the derivative of an antiderivative.

Q: dx = +C (x+1)² X+1

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Q: Find F'(x). 2x F(x) = cos(t*) dt

A: If f(x) is continuous over an interval [a, b], and the function  F(x) = ∫au(x)f(t) dt then F'(x) =…

Q: Let y = f(x), where   f(x) = 5x3/2 + x1/2.   Find the differential of the function.

A: The given function is

Q: Given that y = (In(x))²In(), find dy using the method of logarithmic d.x differentiation. dy %3D

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Q: Find the differential of the function f(x) = (x+4)^(1/2) dy =

A: Find the differential of the functionf(x) = (x+4)^(1/2)

Q: Eliminate the arbitrary constants x = -ln t , y = at + bt^2

A: given  x=-ln t , y=at+bt2 claim- to eliminate the arbitrary constants

Q: 3. Find a af Je ду əx (a) f= sin(3x + 4y) (b) f = tan( 4x + 5y) (c ) f= log(x+ 3y)

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Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x+1) 3- xy + x²y 3 at x = 1

A: Here, We need to find the derivative of the given functions. To solve these questions, we need chain…

Q: dz +y ay dz 100 z= log ( x 100 + x50 y50 + y100 ), Prove that x

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Q: Use Part 2 of the Fundamental Theorem of Calculus to find the derivatives. d/dx ∫_0^x▒〖e^√t dt〗…

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Q: Find y′ by implicit differentiation. e^(x/y)=4x−2y y'=?

A: To calculate the value dy/dx from the provided implicit differentiation e(x/y)=4x-2y. Now,…

Q: Find the derivative of the function: y = In e+2*+1 Oy = x"[(2x(ln x + 1) + 1] y = x*(2 + x + x² In…

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Q: Determine the expression of the integrating function if it is known that: e) S; f(x)dx : - sen(9) +…

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Q: Show that the following functions all grow at the same rate using properties as x co: fi(x) = x°,…

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Q: Integrate the following functions f(x)=Ln [sec (x)] [², 3]

A: We will see the graph of secx to judge the value of greatest integer function of secx.

Q: Suppose w is a function of x, y, and z, which are each functions of t. Explain how to find dw/dt.

A: Given data:"w" is a function of (x,y,z). Therefore, w(x,y,z). And the function x, y and z are the…

Q: Use logarithmic differentiation to find dy/dx. y = (In x)'n ×, x > 1 dy %3D dx

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Q: Let y = (x³ – 4x)(=) Find dy/dx using the method of logarithmic differentiation. Answer:

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)? dx y logy x

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