6. Find dx for each of the given functions using the sum and difference rule. a. y = 5x² – 2Vx + 4 b. y = 2_=-3x 5x 3 c. y = 9x3 + 2x5 - 7x2

Q: > Evaluate the Antegral dx ax45x +2

A: Rewrite the given integrand as follows. 32x2+5x+2=32x+1x+2=22x+1-1x+2

Q: 5. Integrate: [tan(7x)dx

A: 5) The given integral is ∫tan7xdx

Q: Find the derivative. 4 7(+3t) dt 7(P+31)-] 4 dt

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Q: 4) fip by implicit differentiation, where Find dr y + x?y³ = x* + y.

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Q: 5.Use trapezoidal rule to evaluate f,(x² + 1)7 dx by taking n = 4.

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Q: y = 2.16eSin(2x)

A: SOLUTION-

Q: By implicit differentiation, find if y = x2 + 3x + 1 and x = t2 + 2. dt

A: Given,  y=x2+3x+1 and x=t2+2

Q: Find the derivative of O 2sec 2x 2tan 2x O-2 cot2x O 1/cos2x y=In sin 2x

A: I have stated the used formulas in the solution

Q: 2 dx =

A:

Q: Evaluate S sinh x cosh x dx by letting u=cosh x

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Q: Use implicit differentiation to find dy/dx for the function 3x2- y4-y2=4x

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Q: Find the indicated derivative. dp for p q² + 2 5q – 3 %3D dq dp dq II

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Q: Find the derivative of the function. rsin(x) In(2 + 9v) dv Jcos(x) y'(x) =

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Q: Find the derivatives of the functions in Exercis

A: Chain Rule: f(g(x))'=f'(g(x))g'(x) Differentiation formulae: ddxsinx=cosxddxcosx=-sinxddxax=a

Q: (b) Show that 2t cos x and sin x = 1 + ? (c) Show that dt dx 1 +

A:

Q: Find the average velocity of the function over the given interval. y= - 3x? - x, [5,6] – X,

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Q: Find the following derivative. (4* + 8) In x) dx

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Q: Find upper and lower bounds for

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Q: compute the derivative. y = 4 cos(2 − 3x)

A: We know that, ddxcosx=-sinx. Chain rule states that, ddx(f(g(x))=f'(g(x))×g'(x).

Q: Find by implicit differentiation. dx 4x3 + x?y – xy3 = 4 dx

A: Given equation, 4x3+x2y-xy3=4

Q: Find the indic ed derivative. dz x2 for z = x2 dx 1 - x - 2x2 dz dx

A: Formulas:

Q: 4. Use implicit differentiation to find dy when 3x? - 2y = xy dx

A: Given: The equation, 3x2-2y2=xy.

Q: If Va + Vy = 8 and y(25) = 9, find y' (25) by implicit differentiation. Submit Question Jump to…

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Q: Evaluate: 2) x-In x dx

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Q: Find y' by ased proportici Ln Xャ3

A: Taking natural log both side

Q: Find the equation of the tangent line to the function f(x) = ln (7 – 4x) at x = 1. (Use symbolic…

A: Slope of the tangent is obtained by dy/dx

Q: Compute ∫xsin(3x−2)dx.

A: Let the given

Q: Use implicit differentiation to find dx for: x2y3 + 4x5 + 5y3 = 12

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Q: Use an appropriate substitution to integrate 12 x*(x++ 1)°dx

A: The given integral is 12x3(x4+1)9.

Q: If f(x) = cos(2x), which of the equations below describes the average rate of change of f(x) over…

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Q: find dy/dx by implicit differentiation 5x4/5 + 10y6/5 = 15

A: The equation is 5x4/5+10y6/5=15.   Differentiate it with respect to x.…

Q: 4 The range of y =sinx for 7SXS is 2 0syso 4 <ys0 sys1 ys 4 -1sys,

A: We are given a function y(x) = 4/5 sin(x) and we need to find the range of y(x) when π ≤ x ⩽3π2 (…

Q: Find the derivative of f(x)= (Inx Oa 6x(Inx Ob. 4 inx Oc 12(in a Od 24(inx

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Q: 40 XY dy dx

A: In implicit differentiation, we differentiate both sides of the equation.

Q: Find the given derivative. DX 5x -- Dx 5x 1/3 1/3

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Q: show that d/dx arctan (tanhx) = sech (2x)

A: On differentiation, we get

Q: Evaluate ( Sech²(In x) dx

A: In this question we will use basic of calculus i.e concept of integration. First we will convert the…

Q: Find all extreme values for y=x+sinx^2 over [0,π]

A: Given,  y = x + sin2x  We have to find the extreme value in the interval 0, π

Q: Find the indicated derivative. dp for p = dq 1- 9 dp dq

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Q: Find dx by implicit differentiation. y = 5x + 6yx

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Q: Integrate: S dx sin ³x cos6x

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Q: Q2 find the derivative of the following: 1) y = 2stn (5x) 2) y = Inxn cosh 5x ,3) xsin14y = y tan-4x

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost other parts as…

Q: 42 Use implicit differentiation to find y' for 4x*y + In(xy") = 4. Preview

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Q: Calculate the derivative of the following function. 6. 6x y%3= 7x+1 dx

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Q: Please solve and simplify

A: Simplify the given function as follows.

Q: Compute the indicated derivative. U(t) = 5.9t2 + 5.9; U'(4)

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Q: 7 Show that: sech x dx = Sin¹ (tankx) + ( S note: * & Sim'u = dx 1-U² dx Cam multiply sechx by * you…

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Q: Use implicit differentiation to find az/əx and əz/ðy. x2 + 4y2 + 7z2 = 4 dz ax az

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Q: If f(x) = 4 cos x – 6x, find the relative percentage error in f(x) for x=0, if the error in x is…

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Q: If 3x + 2x + xy = 4 and y(4) = – 13, find y'(4) by implicit differentiation. %3D

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