Find the derivative of f(x) = 9 sinh-' (x²) – 9 In ( Vx4 + 1). %3D

Q: Find the derivative of the function. f(x) = In(sinh(x)) f '(x) =

A: f(x) = ln(sinh(x)) here we use chain rule f'(x) = cosh(x)/sinh(x) f'(x) = cot(h(x))

Q: Determine the first derivative of the ff. function dz y = e? sin x + In x (arcsin z) with dx 4

A: Determine the first derivative of the function                   y=ez sin x + ln x (arcsin z)  With…

Q: Can you help me with this problem step by step?

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Q: Explain the method of proving the derivative (dy/dx) of sinh(x) and cosh(x) ?

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Q: 14. If x2 + y2 13, find at (2, 3). dx2 %3D

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Q: Find the derivative of  y=sin^-1(cos(x))

A: We can find the derivative as below

Q: 1. Find the first derivative " if y = x sin 27x . dx

A: Given:  y=x sin 2πxTo determine the firstderivative.

Q: Find the derivative of the function below. y = 5x sin- x + V 16 - x² dy dx II

A: here is the important formulae which is  used to the given problem: 1) d(xn)dx=nxn-12) d…

Q: find the derivative of y with respect to xas appropriate.11. y = ln 3x + x              12. y = 1/ln…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

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: The nth derivative of y = Inx is given by %3D

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Q: Find the derivative of y with respect to x. Y=ln(13x)+x dy/dx

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Q: Find the derivative of the function. y= log sv7x +3 dy dx I3D

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Q: Find the derivative of 3 In xy + sin y = x².

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

A: Find the derivative of y with respect to the appropriate variable.

Q: Find the derivative of the function f(x) = ln(sinh x)

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Q: Find the derivative a) y = x sinh-(x) – Vx² + 1 b) y = cosh-(2Vx +1)

A: The derivative is calculated as:

Q: Find the derivative of y with respect to x if y=∫0ln(3x) sin(6et )dt

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Q: Can you help me with this problem step by step?

A: The given equation,

Q: Find one anti derivative of (x+1)^2 and then find  integral(x+1)^2 dx.

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Q: Find the derivative of ,In sin-1) y = e %3D

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Q: Find the derivative of the function g(x)= integral  x2  tanx  (1/square root 4+t4) dt

A: Leibnitz integral rule for Differentiation :               ddx ∫α(x)β(x) f(t,x) dt = ∫α(x)β(x)…

Q: Find the derivative of y given that y = In (sinh x) %3D

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

A: The three-point midpoint rule to calculate f'(x) is f'(x)≈f(x+h)-f(x-h)2h, where h is the step size.

Q: Calculate the derivative.

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

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Q: Can you help me step by step?

A: Given an equation

Q: Find the nth order derivative of the square root y=√x.

A: Let's first calculate the nth order derivative of the power function y=xm where m is a real number.

Q: What is the derivative of: y = ln ln(1 − cos x)

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Q: Find the derivative. y=cos(ln 4x^6)

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Q: The derivative of y = -ln(cos(ex + 1)) is

A: Our Aim is to find the derivative of y=- ln cos ex+1 -(i)

Q: Find the derivative of y with respect to x. Y=ln(13/x) dy/dx

A: Given, y=ln13x we have to find derivative of y with respect to x.

Q: Use forward-difference formula to evaluate the first derivative of y = cos(x) at x = using a value…

A: Given we have given the function y=cos(x) we have to find the first derivative of y = cos(x) at x =…

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 the function y = x tanh−1 x + ln√(1 − x2)

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Q: Find the derivative of the function g(x) = ln ex/(1 + ex)

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Q: find the derivative of y with respect to x, t, orθ, as appropriate. y = ln (cos2 θ)

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Q: 3. Find the derivative of: y = csch¬(In (sech(sec()))).

A: Note:Two questions submitted simultaneously, kindly upload question 2 separately.

Q: 4x dx

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Q: Find the nth derivative of the function y=xlnx at x=1.

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Q: Find the derivative of the function. 5/1 x+1 In 22 + arctan x %3D X -1· dy dx

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Q: Can you help me with this problem step by step?

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Q: Find the derivative of y with respect to x. y=ln(tan-1(4x5))

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Q: Find the derivative of the function y, below. y = 2x(ln x + In 7) – 2x + V2 dy da

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Q: find the derivative of y with respect to the givenindependent variable. y = log5 ex

A: On simplification, we get

Q: Find the derivative of the function y = tanh−1(sin 2x)

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Q: Find the derivative of y with respect to x.   y= tan-1 *square root (16x2-1) +csc-1*4x ,   x greater…

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Q: find the derivative of y with respect to the appropriatevariable. y = 1/2 sinh (2x + 1)

A: We have to find derivative of y with respect to the appropriate variable: y=12 sinh 2x+1 We know…

Q: Find the derivative of y with respect to x for y = sinh(15 15x ). -1 dy

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Q: Find the derivative of the function f(x) = sinh 9x

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