Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant oft antiderivative.) 2 + t + t2 g(t) G(t) =

Q: Find the derivative of the function. F(t) = e4tsin(2t)

A: Find the derivative

Q: Find the most general antiderivative of the function.(Check your answer by differentiation.)

A: We write f(x) using exponents

Q: Find an antiderivative of the following function by trial and error. Check your answer by…

A: we need to use trial and error method

Q: Find the derivative with respect to x of the function r4x t² F(x) = e dt.

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Q: a. y = x? – x + 1| 1 b. f (x) = 2x+1

A: We have two equations as a function of x . Hence we can differentiate both the equations with…

Q: The derivative dy of the function y = f(x) with dx f (x) = e' (1ª + 2t³) is a) e' (41³ + 61²) + e'…

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Q: (A) Find the derivative of t² – 1 y = t2 + 1

A: The identity used is d(uv)dt=v *dudt-u*dvdtv2 where, u and v are the functions of t.

Q: Find the derivative of the function y = xe2 %3| Select the correct answer below: O e2r (2a + 1) O…

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Q: Find the value of the derivative of the function 2f(x). +3 cas(g(x) at x=1 if f(1)=0, f(1)=1,…

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Q: Find the derivative of f(x) = x²e² A. re* (æ+2) B. x² + 2x C. —xe* (æ+2) D. x²e - 2xe O U A B

A: Given function is fx=x2ex. To find: Derivative of the function. Formula used:  1) ddxxn=nxn-1…

Q: 2 Find the second order derivative of the following functions y = f(x) and evaluate them at x = 2.…

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Q: Find the most general antiderivative of the function.(Check your answer by differentiation.)

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Q: Find the derivative of the function at P, in the direction of u. x- 3y g(x.y) = 2хy +3 Ро(1, - 1),…

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Q: f(x) = 9x3 + 4x.   Find the differential of the function.   dy =?

A: Given , y=fx where fx=9x3+4xwe have to find the differential dy

Q: Do not intergrate

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Q: Find the derivative of the function T(r) = xr* + 5e' + x*. nswer T'(r) =

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Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: 3x-2 1. Z=. ;d'z/dx? (x-1)2 2. Y= (2 – x³ )5…

A: Given: 1. z=3x-2x-122. y=2-x353. y=2x+125

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: Find the derivative (dy/dx) of the following functions: h) у%3D Зx7 —7х3 + 21x2 - i) y = (x² +…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: d²y in terms of x and y, given that 1 x+y Using implicit differentiation, find + 6x = 1. %3D dæ2

A: Here the given equation as

Q: d2y Find at the following point using implicit differentiation: dx2 xy1, (1,0)

A: Differentiate both sides with respect to x,

Q: 2. In each case, find the derivative d (a) z = x* + y and r(t) = In (t) and y(t) = e24, (b) z = 5xy…

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Q: Determine the derivative of the given function: ソ=c 3 y = e x2

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: Find all the antiderivatives of the following function. Check your work by taking derivatives. q(s)…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the most general antiderivative of the function.(Check your answer by differentiation.)   f ( t…

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Q: Find the second derivative of the function. 1+20 (2-0) 20 O d2r de? O d2r 2 1 de? e3 O d2r de? 1 O…

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Q: Using implicit differentiation, find dæ2 in terms of æ and y, given that z+y + 6x = 1. dæ²

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

A: Find antiderivative of the function g(t) (i.e.) G(t).

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: Given  C'x=2x2-3x   ...1C0=4000   ......2

Q: Find the dy/dx of the following function. Implicit differentiation e2y + x3 =y

A: We have to determine derivative of following function

Q: Find dy for the given values of x and Ax. y = x° - 5x + 5; x = 1; Ax = - 0.4 What is the derivative…

A: Here, the given function is: y=x3-5x2+5

Q: Given that f(x) = 9x + x³ + 6, find the derivative of f- by using dy the formula dx 1 Check your…

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: I have stated the used formula in the solution

Q: Find the derivative of the function. g(t) = 1/(√t2 − 2)

A: The given function is ,gt=1t2-2. To find the derivative of the given function. Solution: The…

Q: Find the derivative of f(t) = e+1

A: Given :

Q: h(t) = (e" +2)

A: given that h(t)=(e3t+2)5  So h'(t) = d/dt (e3t+2)5  h'(t) = 5(e3t+2)4 [d/dt (e3t+2)]  h'(t)= 15e3t…

Q: Find the derivative of the function.

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Q: The third derivative of y=x is A) 0 B c) None of the given choices D) 6x E) 3x

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Q: 3. Given x?y? = x² + y², find by implicit differentiation. dx

A: To find: The value of dydx. Given: The equation is x2y2=x2+y2. Formula used: Product rule of…

Q: Find the differential of the function. T =V 9 + uvw

A: Given T = v9+uvw

Q: (A) Find the derivative of t2 – 1 y = t2 +1

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

Q: Find the derivative of the function. g(t) = t2 ln(e2t + 9)

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Q: The derivative of the function y = 2t 1 A V2t 1 2t/2t 1 2t/2t 1 D B.

A: Definition used -            Power rule of derivative -…

Q: x°y- xy? +x² + y² = 0 %3D

A: Use d(UV) = VdU+ UdV

Q: Find the second derivative of the function. f(t) = t?e-5t f"(t)

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Q: A. Find the derivative of the function at o P in the direction of A f(x, y) = x – E) V3sec-1(2xy)at…

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Q: Find an antiderivative of the following function by trial and error. Check your answer by…

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Q: Find all the higher derivatives of the function f(x) = (3x+7)°. TATER P'(x) = P'(x) =] p"(x)=

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