(ii) Hence, by using Leibniz Rule for Differentiation Under the Integral Sign, compute the value of con® cos (: sin 0) a0.

Q: Find the first derivative of 2cos(2 + x³). a. -6x² sin(2 + x³) b. -x² (sin 2 + x³) c. -6x² (cos…

A: daf(x)dx=adf(x)dx ; where , 'a' is constant. dcos (ax)dx =-a.sin(ax) dxndx=n.xn-1 .

Q: The first derivative of y = cos(3x-8) is O a. - sin( 3x-8) O b. 3 sin( 3x-8) O. - 3xsin( 3x-8) O d.…

A: Given function is, y=cos3x-8.   It is differentiated as follows: dydx=ddxcos3x-8

Q: Find derivative of the following functions 1. y= sin^-1 2x^2 2. y= tan^-1 2x^2/5

A: Given 1. y=sin-1(2x2)2. y=tan-1(2x25)

Q: 1. Given that x cosx dx = x sin x+ cosx + C By using the differentiation, verify that the given…

A:

Q: Find the derivative of cos(xy^2) = -3y using implicit differentiation

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Q: 7. Find the derivatives of y = cos- (sin(2x)) (show work)

A: Using derivatives of composite function. Or Using trigonometric transformation.

Q: Find the first derivative of  y = (x – 1) √ (2x – x2)   + arcsin (x – 1), and y = arctan [ (3 sin x)…

A:

Q: Use implicit differentiation to find: (sin3.14x+cos3.14y)2=2

A: Consider the given equation.

Q: The slope of the tangent line to the curve at the point where x = O +1 -1 DNE f(x) = sin² x cos²x

A: The slope of the tangent line to the curve  y = f(x) at the point x= k is f '(k)

Q: Find the derivative of f(x)=sin sin(5x

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Q: How do I verify d/dx(cos^-1(x))=-1/(sqrt(1-x^2)) using implicite differentiation?

A: Verify the result by implicit differentiation as follows.

Q: Find the second derivative of ƒ (z) = 6 sin (5z). Enclose arguments of functions in parentheses. For…

A:

Q: 1 Using implicit differentiation, prove cot"x -- Make sure to show all work. dx 2 x* +1

A: Let  y=cot-1x Therefore: cot y=x

Q: 1) Find 4 by implicit differentiation given 4 cos x sin y = 1. dx

A: Differentiate above equation with respect to x.

Q: What do the limits limh→0((sin h)/h) and limh→0((cos h - 1)/h) have to do with the derivatives of…

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Q: Find the differential of z = sin²(5x) + ev

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Q: integral of sin^5(3x)cos^3(3x)dx

A: The integral of ∫sin5(3x) cos3(3x) dx is sin5(3x) cos3(3x). If we need to find the integration then…

Q: Find the critical points/number of the function h(x) = e^x sinx-sinx+cosx by applying derivatives.

A: First calculate its derivate then equate it equal to 0 to obtain the critical points. h(x)=exsin…

Q: MA 181 1i SinGt) + 3xy% - (osy= e?

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Q: Use forward-difference formula to evaluate the first derivative of y = sin(x) at x = O 2√2 π -2√2 ㅠ…

A: Given that y=sinx. We have to find the first derivative of y=sinx at x=π2 using a value of h=π4 by…

Q: 3. Use implicit differentiation to find an equation of the tangent line to the curve sin(x + y) = 2x…

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Q: Find the tangent line to the function f(x) = 2x cos4(x) at the point (0,1)

A: We have given function fx=2xcos4x and point 0,1. We have to find tangent line to the function at the…

Q: Use chain rule of differentiation to find  Y is equal to 3x²-5x +12 X is equal to 2u²-5u +11 Find…

A: Consider the given function asy=3x2-5x+12 And x=2u2-5u+11

Q: Find y' by direct differentiation (with respect to x). y = 10etan(x) and y = (x3 + 4) sin(x)

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Q: 1. Find the derivative of the following sin² x cos² x a)y + 1+cotx 1+tan x

A: We have to find derivative of given trigonometric term.

Q: The derivatives of sin- 1 x and cos- 1 x are negatives of each other.

A: From the question it's not clear, what do you want us to do with it. I assume that you want to know…

Q: 4. Use implicit differentiation to find an equation for the tangent line to the graph of sin(x +y) =…

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Q: Prove the differentiation formula d/dx [cosh x] = sinh x

A: We use the formula of coshx to find the derivative

Q: 17. Find the first derivative for J(x)=tan0x sec0

A:

Q: 2. Use the implicit differentiation to find an equation of the tangent line to the curve at the…

A: Given curve ,yesinx=xcosyNow using implicit differentiation , we…

Q: 19. y = sin-1+ cos-1 2 2

A:

Q: Find the second derivative of f (z) = 6 sin (5z). %3D Enclose arguments of functions in parentheses.…

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Q: ∫ (1 + secx)2 dx Evaluate indefinite anti-differentiation

A: Solve it

Q: Verify the formulas by differentiation. ∫ 1/x + 1 dx = ln | x + 1 | + C, x ≠ -1

A: We have to verify by formulas of differentiation where expression is given as: ∫1x+1dx=lnx+1+C, x≠-1…

Q: Find the second derivative of f (x) = 9 sin (2æ). Enclose arguments of functions in parentheses. For…

A: Second derivative of f(x) is given below...

Q: Use a central difference method to approximate the first derivative of cos(x) at x = pi/3., assume…

A: To approximate the first derivative of fx=cosx at x=π3 by taking the value of h=0.01.

Q: sinx In (2) co cos x

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Q: -1/7 17 dx =?

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Q: Use differentials to estimate sin (π/6 + 0.01).

A: Use differentials to approximate the value of sinπ6+0.01 The nearest number to sinπ6+0.01 whose sine…

Q: Find the second derivative of f (z) = 6 sin (4z). %3D Enclose arguments of functions in parentheses.…

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Q: 8) Use implicit differentiation to find y', given cos(x+ y) = y² sin x

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Q: 1. Explain how to use the differentiation part of the Fundamental Theorem of Calculus to determine…

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Q: 4. Use implicit differentiation to find az in xexyz sin(2z) – xyz = 5. ду

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Find the indefinite integral and check the result by differentiation. COS X 1 - cos²x dx

A: Recall; sin2x+cos2x=1

Q: 3. Find if y³ + 2xy - x² = cos x using implicit differentiation.

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Q: Use implicate differentiation to find if yz = cos(x-52) %3D

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Q: 15)S (VA +) dx

A: We are authorized to solve only 1 question, please repost remaining questions

Q: Verify the differentiation formula.

A:

Q: Solve for the derivative of the Trigonometric Differentiation. 1. y = sin (5x) + 3x cos (5x) 2. y…

A: given y=sin5x+3cos5xdiffrentiate w.r.t. xdydx=ddxsin5x+3cos5xdydx=ddx(sin5x)+ddx(3cos5x)we know that…

Q: Find the derivative of a. (e(sin2x))/[In(cos2x)]2

A: We have to find out derivative