What main derivative rule does each integral bring to mind as you think of an antiderivative? Example S sin(t?)t dt d cos(inside) = - sin(inside)· · d inside dt dt

Q: Using the concept of the derivative of sin x, what is the antiderivative of sin x? -2 cos x + C 2…

A: We know that: ddx(cos x)=-sin x...(1)

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

A: Given,f(x) = 6x + 8cos(x)Antiderivative is given by,∫ f(x) dx = ∫(6x + 8cos(x)) dx∫ f(x) dx = 6∫x dx…

Q: two rates are related using y=x^2+3. find the derivative when x=1 , given that dx/dt = 2 when x=

A: Given that: y=x2+3

Q: What is the derivative f'(x) of: f (x) = elő e-t²dt (We are in te subject of Logarithm and…

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

A: Given,           Antiderivative of fx=2x+8sinhx

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

A: To find the anti-derivative of the given function.

Q: at main derivative rule does each integral bring to mind as you think of a Example S sin(t²) t dt d…

A: See the details solution in below

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

A: Now,

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

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Q: Find the derivative of y with respect to 0. y sech P. sech 1. 5. (Type an exact answer, using…

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Q: c. h°(3 – 2h²)7 с.

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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: b. 2ye?y

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Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: We first integrate it ∫e-x+4xdx=∫e-xdx+4∫xdx=-e-x+4x22+C=-e-x+2x2+C   C=integrating constant

Q: The Integration by Parts Formula is obtained from which differentiation rule? O The Power Rule. O…

A: The integration by parts Formula,_________is obtained from which differentiation rule.

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: Evaluate ∫(x+1)dx

Q: Exexcises E Set 2] Implicit Differentia tion x=x 2. Find dy if dX 1. +Sin xy Find dy if 2x²- 3y'=8…

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Q: Find the derivative. sin 0 d. secy dy de a. by evaluating the integral and differentiating the…

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Q: dy • Use the Product Rule, the Chain Rule, and Implicit Differentiation to find where x and dx y are…

A: On the right side, we use the chain rule. On the left side, we use the product rule and chain rule…

Q: SCALCETS 5.3.013. MY NOTES ASK YOUR TEACHER 3. Use Part 1 of the Fundamental Theorem of Calculus to…

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Q: Refor to Hhe imaga below EValuate the Particular soluțion differential equetion and find X when yeof…

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Q: Calculate the derivative of y with respect to x. Express derivative in terms of x and y. e5xy = sin…

A: Explanation of the answer is as follows

Q: d Find the derivative e" + sin ax] dx e" – a cos (ax) e" + a sin (ax) e" + a cos (ax) e" + sin (ax)

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Q: B- The derivative is y = ln (sec (In 0)) In 0 sec 0 O it is O it's In 0 cos 0 an O another answer…

A: See the details solution in below

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: Given:∫x+3x  dxIntegrating formula:∫xn dx=xn+1n+1+CIntegration properities:∫fx+gx dx=∫fx dx+∫gx dx∫c…

Q: Guess an antiderivative for the integrand function. Validate your guess by differentiation and then…

A: Definite Integration

Q: (c) Find - (2x sin 2x + cos 2x) and hence evaluate J: (x cos 2x)dx dx

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Q: Integral sign with 1/2 on top and 0 on bottom:  x cos Pi x   dx

A: To evaluate

Q: 1+cos x Determine the indefinite integral of f : dx. x+sin x

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Q: Find the derivative. cos X d 13t12 dt dx a. by evaluating the integral and differentiating the…

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Q: Find the derivative. d sin 13t dt dx 2 a. by evaluating the integral and differentiating the result.…

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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: d cos a In(x + a) dx da sina

A: Given ddα∫sinαcosαlnx+αdx

Q: x = 1+ 2cost + cos(2t) = 2sint + sin(2t) curve given a) Take the derivative of x and y according to…

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

A: f(x)=5x+3cos(x)Formula:∫xndx=xn+1n+1+C∫cos(x)dx=sin(x)+C

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: We have to find indefinite integration and we have to check it by differentiation: ∫-5 sin tdt We…

Q: Both x and y denote functions of t that are related by the given equation. Use this equation and the…

A: Given y=5x+3

Q: Calculate the derivative of y with respect to x. Express derivative in terms of x and y. e6xy = sin…

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Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

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Q: Find the derivative of f (w) = 6 ln (w) + 15. Enclose arguments of functions, numerators, and…

A: f(w) = 6ln(w) + 15  Differentiating both sides w.r.t x, we get,

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

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Q: Derivative OF the FollOwing 1.y sin x)* 2. y-Tex te* 3. d dx ( scextanx t in csccxttanx)

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Q: *Show all work (or provide a brief explanation) clearly, and in order, to receive full credit for…

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Q: etermine the instantaneous rate of change of the function πt √√x sin (772³) dt : x = 1. x3 1 + √t

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Q: dy Use implicit differentiation to obtain if given dx -1 e¤¬y + cosh(2x) + tan¯¹ x = π.

A: The implicit functions are represented as: f(x, y)=k, where k is a constant. The explicit functions…

Q: - Ose the tranfiorms from the "Table of Lapiace Transformso fnd the Lpce of the function below. You…

A: Given problem:- Find the laplace transformation of f(t) =(1+t)3

Q: Find dy/dx using appropriate derivative rules. (don't simplify) 1. y=x^2/3 log4(x)

A: We are answering only the first question as per our honor code. Given, the expression y=x23log4(x),…

Q: Q5: The Derivative of sinh- (tan x) ? O tan(x) O sin(x) O cos(x) /sec(x)/

A: 5) The given function is sinh-1tan x.