Find the derivative of y with respect to x. y = tan 1 (In 4x) 1+ (In 4x)2 xV1+ (In 4x)² x(1 + (In 4x)²) x(1 + (In 4x)²)

Q: Evaluate the derivative of y = cos '2x - In 1-4x, where x = 0.125 -12> 2

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

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Q: In xy = x² + sin xy

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Q: Use three-point midpoint formula to evaluate the first derivative of y = cos(x) at x = 5 using a…

A: Given function is y=cosx. We have to find the first derivative of y=cosx at x=π2 using a value of…

Q: find the derivative of y with respect to the appropriatevariable. y = ln (x2 + 4) - x tan-1 ( x/2)

A: We use the chain rule and product rule

Q: Find the first derivative of g(x) = - 9e* tan(x). : (x),6

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Q: Find the derivative of y with respect to x. 2x + 3 26) y = sec = sec-1 27) y = -sin-1 (5x2 + 2) 28)…

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Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 x - x sech-1 x

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Q: The derivative of In (cos x) is

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Q: Find the derivative of y with respect to x of y = xlnx – x.

A: Using rules of differentiation.

Q: find the derivative of y with respect to the appropriatevariable. y = x sin-1 x + √(1 - x2)

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Q: Find the derivative of y with respect to x. 1 y = cot 16x² - 1 + sec - 1 2 - 1 4x, 4

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Q: In(5æ) Find the derivative with respect to x of y = %3D 5x y' = | %3D

A: Find the derivative

Q: 2. Use implicit differentiation to find the derivative of y with respect to x for the following: xe…

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Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 (1/x)

A: To find dydx, rewrite the equation and then differentiate with respect to x.…

Q: Find sixth order derivative of the function f(x)=(x-5)^7.cos(5x) by using Leibnitz theorem.

A: n! = n × (n-1) × (n-2) × (n-3) × (n-4) × ............ × 1

Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = π/4 , g'(2) = 5, and g"(2)…

A: singx

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In(In 9x)

A: The solution for the above question is as shown below.

Q: Find the derivative of y with respect to x.

A: Assume z=x^5+1. Then found derivative dy/dx using the chain rule.

Q: Find the derivative of y with respect to x. y = 5x4 sin-1 r 1 V1-x? + 20x3 5x4 1+x2 + 20x³ sin¬1 x…

A: We have to find the derivative.

Q: Find the derivative of the function. y = 3 x tanh-1 x + 3 In/1 - x2 y' =

A: Product Rule of Differentiation : d(u.v)dx = u.dvdx+dudx.v

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x (x+ 3)5 15) у - In 6х- 8 A)…

A: Given that:y=ln1-xx+35To find derivative

Q: Find the derivative of the function.

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

Q: Find the derivative of y = In (tanh x).

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Q: Find the derivative of y with respect to X. y = tan 1 5x 105x(1 + 5x) 2(1 + 5x/5x J1- 5x 1+ 5x

A: It is derivative.

Q: Find the derivative of r = In (cos" x).

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Q: · f(x) = sin(In r²) %3D

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Q: Find the derivatives of the functions in Exercis

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Q: Find the derivative of y with respect to x. -1 y = tan (In(2x))

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Q: Find the derivative of y with respect to x. 1, 1+x2 In 1- x3 y

A: If you have function f(x) in the numerator and the function g(x) in the denominator, then the…

Q: Find the derivative of the function: f(x) = [sin(4x + x)] [cos(x4 + 4)] f(x) = e3x²+*(cscx + secx)2…

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Q: Find the derivative of f(x) = e" – a3 +In(x) - In(x)

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Q: Find the derivative of y with respect to x. 2x + 3 26) y = sec-1

A: Let, z=(2x+3)/5   We differentiate using the chain rule

Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = 4, 8'(2) = 5, and g"(2) =…

A: Given: The function singx with g2=π4, g'2=5, and g''2=3, To find: The second derivative of given…

Q: Find the derivative of y with respect to x. y = In (tan -1 (9x5))

A: Given : y=lntan-19x5

Q: Find the derivative. y = In(x²)tan (3x) %3D

A: Given:

Q: k(x) = x In x %3D

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Q: e derivative of y with respect to x. y= 2sin^-1(5x^4

A: we have to find the derivative of y with respect to x.y=2sin-1(5x4)

Q: Find the derivative. 8 + e y = In 8 + et 8 - ex.

A: Given,          y=ln8+ex8-ex

Q: find the derivative of y with respect to x, t, or θ, as appropriate.

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Q: Find sixth order derivative of the function f(x) = (x – 5)7.cos(5x) by using %3D Leibnitz theorem.

A: If y=uv where, u and v are functions of x then un and vn denote the nth derivative of u and v with…

Q: (x² +SJ° In 14-X つ. dr

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Q: Find the first derivative of g(x) = 2 In(x)tan(x*). g'(æ) = %3D

A: Given that g(x) = 2ln(x) tan(x^4). Find first derivative of this function. We know that derivative…

Q: -5

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Q: Find the derivative of y with respect to x. 58)y tan (In 2x)

A: Firstly, we use the result that  derivative of inverse of tan of x is 1/1+x^2

Q: Find the derivative of y with respect to x. y= In (tan (4x*))

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Q: Can you help me step by step?

A: Given function,