Differentiate g(x) = (In(x² + 1) – tan-ª(6x))10

Q: (5x) S sin(x) tan(x) .........

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Q: [In(x²)-ex cos(x-1).tan(Tx) 20. lim 2x2-x sin2(1-x) X-1

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Q: Let y=sin2x. Differentiate this function without using the chain rule.

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Q: Integrate sin^2(7x)-cos(x)

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Q: SOLVE USING VAREATION Of PARAMETERS OR REDUCTION of ORDER 2 tan'x

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Q: Determine the absolute extreme values of the function f(x) = sinx - cosx + 6 on the interval 0 ≤ x ≤…

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Q: Find the derivative of g(x) = In(sin²(ed/x)).

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Q: Find the derivative of f(x) = 2 tan^-1(x) 6^x

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Q: Differentiate. y = In Sin x  - 1/2Sin2 x

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Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: Differentiate: (etan(x)) /(1+x)  Show all working out.

A: Given  etanx1+x. We have to differentiate it. Used formula:- ddxfxgx=gx⋅ddxfx−fx⋅ddxgxgx2 Here,…

Q: Find the derivative of g(x) = 4x tan x.

A: The given function is: g(x)=4x5 tan(x)

Q: 3x-x Tan 1-3x? х-х

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Q: Find the derivative f'(x): f(x)=x4-x2+sin-1x/3 **4-x2 is under a radical sign!

A: Consider the given function f (x) taking (4-x^2) under the radical sign. Differentiate f (x) w.r.t x…

Q: Express in exact form: In(x² + 1)dx

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Q: What is the first derivative of g(x) = In 4x²+4x+8 ? x 3 tan x

A: we use Logarithmic properties

Q: Find the slope of the graph of the function at the given point.

A: We have the given function as fx=4x5+3x-sinx          ⋯⋯1 As we know that, slope of a function fx is…

Q: 2tan x In (cos x) dx=

A: here we have to integrate the given integral.

Q: Find  y''  by implicit differentiation. 4x2 + y2 = 4

A: Given,  4x2+y2=y,we have to find y''Differentiate with respect to x,we get…

Q: 6. Differentiate. a) f(x) = In (sin²x) b) g(x) = In (xe-2*)

A: Write sin2x as (sinx)2 and simplify the terms and use the log property to simplify the term and…

Q: Find y' by implicit differentiation. 1) x²y° = 2

A: Given equation: x2y9=2 To find: y' by implicit differentiation.

Q: Let f (x) = sin−1(x^2/6)− tan−1(12x + 1). Find the derivative of f.

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Q: Find the critical points of f (x) = 2 cos 3x + 3 cos 2x in [0, 2π]. Check your answer against a…

A: Given: f(x)=2 cos(3x)+3 cos(2x), 0, 2π

Q: tan (5x) x sin3 (2x) 2)- limx-o:

A: we have to evaluate the A=limx→0tan4(5x)xsin3(2x)

Q: Find y" by implicit differentiation 2x2y2=

A: Find y’’ by implicit function2x2+y2=6      ………(i)

Q: Compute Each Derivative: 1) d tan¯¹ (1 + e²x) dx 2) x²cos-¹(3x4) d dx 3) x(sin-¹(x))² dx

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Q: On the graph of f(x)=tanx and the interval [−2π,0), for what value of x does the graph meet the…

A: To Determine: What value of x does the graph meet the x-axis. Given function is :…

Q: f(t) = In Itsinx 1-sin x g(x) = x sin ¹3x + √1-9x² G(x) = x In (9 + x²) + 6 tan-¹ (-)-2x

A: Note: Since, in the first function there is a typing error "f(t)", it should be "f(x)" because it is…

Q: Find the slope of the graph of the function at the given point. f(x) = 4x5 + 2x - sin(x), (0, 0)…

A: We havefx=4x5+2x−sinx

Q: Lim as x approaches 0  1-cos(5x)+sin(3x)/x

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Q: y" + 2y' = sin 2x ||

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Q: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

Q: Find the smallest positive zero of f(x)=cos^2(x)-sin^2(x)

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Q: 3. Evaluate f x sin2 (x²) dx.

A: Given I=∫x sin2x2 dx To Find I

Q: Find constants c1 and c2 such that F (x) = c1 sin 3x + c2x cos 3x is anantiderivative of f(x) = 2x…

A: Given: Fx=C1sin3x+C2cos3x and the antiderivative of F(x) is fx=2x sin3x To find the constants C1 and…

Q: Find and locate the local and absolute extreme values of f(x) = x+(sin2x) in [0, π].

A: Find and locate the local and absolute extreme values of f(x) = x+(sin2x)in [0, π].

Q: Find the slope of the graph of the function at the given point.                         f(x) = 4x5 +…

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Q: Find the 2nd derivatives

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Q: Find the derivative of f (x) = arcsin (x²). 2x f' (x) = 1-a4 f' (x) V1-x4 2x O f' (x) = V1-a² O f'…

A: Use differentiation of trigonometric function

Q: Find the derivatives of inverse function: y = sec-1squareroot of 1 + x2 AND…

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Q: Find the derivatives of Tan 1 V1+x -1

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Q: f (x) = 4 sin(3x + 7) is continuous at every point x = x0; that is, lim 4 sin(3x + 1) = 4 sin(3xo +…

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Q: Find y" by implicit differentiation. 3x" + 4y - 2

A: differentiate it with respect to x.

Q: limit x to 0 3x-3xcox/sin^2(3x)

A: Here given limit as Use the L'hospital rule which states

Q: Find the derivative. Simplify completely. 1. f(x) = 4x³ cos x 2. g(x): Sx-4 In x 3. у sin x 4. f(x)…

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Q: 6x 2) = 4 y7

A: 2) Given- 6xy7=4 To find- The derivative of the above expression using implict differentiation.

Q: Differentiate the following functions 4 1-cos2x Y = by chain rule. 1+cos2x

A: To differentiate the given function.

Q: f(x) = In(sin² x)

A: Given,           fx=lnsin2x

Q: Find y' by direct differentiation (with respect to x). y=-x2+2x5-e-6x

A: Since you have asked multiple questions in a single request, we would be answering only the first…