Evaluate ( Sech²(In x) dx

Q: Find the derivatives of the functions in Exercis

A: Differentiation of the rational function can be done with the help of the differentiation formula…

Q: Find the Derivative f(x) = cosh(In(4x))

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Q: Find the derivative of ƒ (x) = /7– 8x. %3D To enter va, type sqrt(a). f' (2) =

A: We have to find the derivative of the given function.

Q: sec 3x tan² 3x dx

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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: Use the Power Rule to compute the derivative.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the derivative. y = 7x² – sinhx %3D

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Q: compute the derivative f (x) = ln(4x2 + 1)

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Q: Differentiate with respect to the independent variable: y=tan[ln(3x2+5)]

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Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

A: To calculate the integral

Q: 2x2+x dx x+1

A: Integration ∫2x2+xx+1dx

Q: Determine the first derivative of the ff. function 1 + In(3x?) y : 1+ In(4x)

A: the given function is: y=1+ln3x21+ln4x we have to determine the first derivative of the given…

Q: 4) Use the quotient rule to find the derivative. Simplify the result. d dx |3x – 4

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Q: Find the anti-derivative of: S(3x* – 6x)° (2x³ – 1)dx

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Q: Verify the formulas by differentiation. ∫ sec2 (5x - 1) dx = 1/5 tan (5x - 1) + C

A: ∫sec25x-1 dx=15tan5x-1+C

Q: Compute the derivative. f (x) = (2x4 − 4x−1) sec x

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Q: 1. у %3D 4x? — Зх — 2.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Verify the formulas by differentiation. ∫ (3x + 5)-2 dx = -(3x + 5)-1/3 + C

A: Given ∫(3x+5)-2dx=-(3x+5)-13+C Verify the formula by differentiation Consider Right hand side value…

Q: find integral sqrt (1 - 4x 2 ) dx

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Q: Find the derivative f(x)= In(ex+9)

A: find the derivative

Q: Use Integration by Substitution to find sin(x²) 2x dx

A: As per our guidelines we are supposed to answer only 1 question. Please repost other questions as…

Q: use the Power Rule to compute the derivative.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the derivative. 5х + 1 In 5x - 1 dx 5x +1 %3D dx 5x -1)

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Q: Verify the differentiation formula.

A: Given Data The differentiation formula is .   The formula of sech x is, The left-hand side of the…

Q: Find first and 2nd derivative guncic 2 tan2x 3.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: 1 dx Ji x/1- (In x)²

A: ln x = tdxx = dtx=1 → t = ln 1, t=0x=e → t = ln e, t=1   I = ∫01   11-t2  dtFormula:∫ 1a2-x2  dx =1a…

Q: Excrcise 10. Find the derivative d -7x * [" (t³ + 2) dt dx

A: Given,          ddxx∫57xt3+2dt

Q: Evaluate: 2) x-In x dx

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Q: d Use quotient rule to prove [cscx] = -cscxcotx. dx

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Q: 9. y = 3x – Vx

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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: Find the derivative of n'n(cosu). Where n=666.

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Q: Find the derivative 3x (x4+ 1)5 dx d 3x (x4 + 1)5]- dx

A: To find the derivative of [3x·(x4 + 1)5]

Q: find integral  sqrt ( x2 - 9 )dx

A: Given: I=∫x2-9dx we know that ∫x2-a2dx=x2x2-a2-a22lnx+x2-a2+c                                ..1

Q: Verify the formulas by differentiation. ∫xex dx = xex - ex + C

A: We have to verify by differentiation that ∫xex dx=xex-ex+C We know formula of differentiation,…

Q: Find the first derivative by applying the appropriate rules. DO NOT SIMPLIFY the algebra. (a) fx)…

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Q: Use the rule for reciprocals (수) - - to find the derivative: d 1 %3D dx lx2 Зх + 2

A: Given the rule of reciprocals as 1f'=-f'f2. It is required to find the derivative of 1x2-3x+2. Note…

Q: 7. y = Vx + 2

A: Using Delta method differentiate y. And using rationalising.  Follow step 2nd  .

Q: Find the derivative of ƒ (x) = cos-1(In(4x²+1)).

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Q: Use the Power Rule to compute the derivative.

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Q: Find the second derivative y=lnx + 3 sin(4x) d²y dx² of

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Q: 1. y= ArctanB %3D 3-V9-x2

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Q: 8. y = va? + x²

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Q: Find -by implicit differentiation. dx 6xe + ye" =7 ت ب تھج( + ex

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Q: dx 2 x--1

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Q: 7. y= ln 2x³ 5х-3

A: Explanation of the answer is as follows

Q: s(w) = In( w - %3D

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