If g(x) = In(6x6 - 2), then the derivative of g'(x) is 676 36z5 1 6x5 626 36x5 1. 3675 1 6x6 O O

Q: What is the first derivative of s(x)=(7x)3x at x=4?

A: To evaluate s'(4)

Q: find derivative of g(x)=integration3x2x (u2-1)/(u2+1) du

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Q: In y = 22 cosh1 2x

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Q: 2. (a) Find the derivative of f(x) = 2x2 – 2x + 2 from first principle sin x (b) If y = x + find x4…

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Q: When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .

A: Given Data The function is f(x,y)=3xy²-xᶟ.   Differentiate the function f(x,y)=3xy²-xᶟ with respect…

Q: Shows the derivative function of: 2x² + ln x²(2x² + 5x − 1)

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Q: calculate the derivative with respect to x. ln(x2 + y2) = x + 4

A: Given function lnx2+y2=x+4 Differentiate the above function w.r.t 'x' ddxlnx2+y2=ddxx+4…

Q: 4. Calculate the derivative of the given function directly from the definition of derivative y = v2x…

A: Given function is  y=√(2x+1)

Q: Find the derivative of ƒ (x) = 5ª In (x).

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Q: Find the derivative of y with respect to x if y = (11x2 - 22x+ 22) ex.

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Q: Compute the derivative of f(x) = 7 ln (x + 10) + In (x³ ): Answer: f'(x) =

A: Given function is  f(x)= 7ln(x+10) + ln(x3), we have to find the derivative of f(x) with respect to…

Q: Solve for the derivative of the Hyperbolic Differentiation. 1. y = ex cos h 2x 2. y = ln sin h x…

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Q: Find the derivative of Ox²2cosx + 2xsin x O 2xcos x O x² sin x + 2xcos x O x2cosx y=x²sinx

A: We know that if f(x)=g(x)h(x) then  f'(x)=g'(x)h(x)+g(x)h'(x)

Q: Compute the derivative of y = ln ( – V1 – 2 cosh x (x° + 2) |

A: To compute the derivative of,  y=ln1-2 cosh x .x3+2x.x-1.

Q: Obtain the second derivative of the function f(x) = 6 In(8x) – 3z4 and state the value of this…

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Q: What is the first derivative of q(x)= ln((7x^2+3x+7)/((x^5/6)(tan(x)))

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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: 2. In y = 2" + x cosh 2x

A:

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

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Q: Find the derivative of ln(2x2)+ln(2x)+1/3 where x=1

A: Given,           The derivative of  ln2x2+ln2x+13 where x=1

Q: S(x)= Jx-5

A: given that f(x)=1x-5 find the derivative from first principle f'x=limh→0 fx+h-fxh

Q: Find the derivative: y = 6 In x 6 ln x-1 x7 1-6 ln x 12 1+6 ln x x12 4 O 1-6 ln x x7 O

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Q: Compute the derivative of the fo f(x)= 2x+3x ex

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Q: Find the derivative of y= ln (6X^2+3X)^3/(7X-2)

A: Topic-Derivative

Q: Find the derivative of the function.

A: Consider the given function as y=xtan-12x-14ln1+4x2

Q: Compute the derivative of ln r3 –1 V2x+5x²

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Q: In 2x y = - cos x

A: ddxln 2xcos x= ddxln 2x . cos x - ln 2x.ddxcos xcos2 x= 12x. 2. cos x - ln 2x.(-sin x)cos2x= cos xx…

Q: Find the derivative of x2cosx+2xsin x O 2xcos x O x² sin x + 2xcos x Ọ xzcosx y=x²sinx

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Q: Find the derivative of fcx) = en (sinh Cx)) 5

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Q: Find the anti-derivative of: f(3x^3+9x)^6 (x^2+1)dx

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Q: What is the approximate derivative of f(x) = x2e* , using backward-difference approach at %3D x-2…

A: The main objective is to calculate the value of the derivative of the function f(x)=x2ex at the…

Q: 1. 8rd Derivative of fC x) = 4 x³ - 8x5 1

A: We will use just the basic knowledge of differential calculus to answer this question step-wise.

Q: Find the derivative of f(x) = –4 ln (5 cos (-4x))

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Q: Find the derivative of flx) = x 1x \ - Does plo) exist

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Q: Find the derivative of the function y, below. 9x(ln x + In 2) – 8x + v2 %3D

A: first, simplify the function  y=9xlnx+ln2-8x+2 y=9xlnx·2-8x+2 y=9xln2x-8x+2

Q: Find the derivative of ƒ(z) = ln2x 1. 2z

A: We first expand using the addition property of log.

Q: Determine the first derivative of the ff. function a. y = 400(2)*+3 sin 3x b. y = Vxe2x cosx…

A: Given1) y=400(2)x+3sin3x2) y=xe2xcosx3)y=1+ln(3x2)1+ln(4x)We need to find the first derivative of…

Q: he first derivative of f(x) = ln(5X4 - 6x) will be

A:

Q: What is the first derivative of f(æ)= ln(3z²+7z )? 5z

A: Given  f(x)=ln3x2+7x5x We know that derivative of ln(x)=1/x…

Q: is the derivative of In

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Q: Shows the derivative function of: x³  + ln x(3x² + 5)

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Q: 2) Use logarithmic differentiation to find the derivative (Vx + 3)(x – 7)5 f(x) : (x3 – 4) - -

A: Given function is fx=x+3x-75x3-4 Given function can be re-written as: y=x+3x-75x3-4 Taking logarithm…

Q: What is the derivative of y (2æ)* O (2x)^(x) (1-2 In2x) O (2x)^(x) (1-In2x) O (2x)^(x) (1+2 In2x) O…

A: Given; y=(2x)x.

Q: Find the first derivative: In 2x f (x) 1- In 2x f(x) = In (sec x) f(x) = cos (In x) f(x) = In[cos…

A: we can answer only three subparts, or the first question and the rest can be reposted. No more than…

Q: 8. Find the derivative of y = In(3t) dt.

A: To Determine: Find the derivative of given integral:…

Q: find the derivative of f(x)=sec(x^4)ln(9x-8)

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Q: Find the first derivative of h(x) if h(x) = cos (x – 2x) -

A: h(x) = cos2(x3-2x)

Q: Show that the derivative of f(x) =xln(x)−x is ln(x). Use this to compute∫ln(x)dx.

A: Sum/difference rule of differentiation,

Q: Find the second derivative of y=x-1 at x=2

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Q: 3) Determine the second derivative of y = 5x* + 4x -+÷-3 2x2

A: