find derivative    1.y = ln (cos^2 u)     2. y = ln (3te-t)    3. y = e^(cos t + ln t)

Q: Find the derivative of the logarithmic functions: y = ln (tan^2 θ )

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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: Find the derivative. Simplify where possible. hx) = (1 - cosh x) /( 1 + cosh x)

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Q: Find the derivative of y with respect to theta. y = ln(sec(ln(14θ))).

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Q: Find the derivative of sinh(x)tanh(x).

A: As per our guidelines I am solving only first problem please repost other question.  y = sinh(x).…

Q: Find  dy dx by implicit differentiation. tan−1(4x2y) = x + 5xy2

A: tan−1(4x2y) = x + 5xy2 We differentiate both sides with respect to x using the product rule and…

Q: Find the derivative of function and simply it whenever possible y= ln(ln sec x)

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Q: 45. y = cos vsin(tan x)

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Q: Find 3rd order derivative of y with respect to x , if x = a sint, y = b cost.

A: Given: x = a sint y = b cost -------------------------------------------------- To find: 3rd order…

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. Simplify where possible  y = cosh (ln x)

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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: if u:X- COSX and V=X+ Cosx find the derivative du

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Q: Show that the derivative of the function sinh -¹ x can also be obtained by letting y = sinh -¹ x and…

A: Soln:To find the derivative of sinh-1x

Q: Find the equilibria of the differential eq

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Q: Find the anti-derivative: x2/3 dx. Upload Choose a File

A: Using simple integration method to solve the question.    Attached below is the detailed solution.

Q: derivative of y = arctan(x2+ 3)

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Q: 2. Use logarithmic differentiation to find first derivative of y (sinx)r

A: Formula used: ddx[u(x)v(x)]= u(x)v(x).ddx[ln(u(x)).v(x)] ddx(u.v) =dudx.v + udvdx

Q: .Find the derivative of the function y = cosh*x- sinh“ x

A: As per guidelines we can solve only one question at a time, if you need more answer kindly repost…

Q: Find the derivative of y = tan 3x

A: Given function is: y = tan 3x We have to find the derivative of y with respect to x.

Q: Find the first four derivative  if  y= cosx

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Q: , find the derivative of y with respect to the appropriate variable 21. y = ln cosh y - 1/2 tanh2 y…

A: (21) Consider the provided equation, y=lncoshy-12tanh2y Find the derivative of y with respect to the…

Q: In(cos(x)) cos(In(x)) Find the derivative of

A: Quotient Rule of differentiation: ddxuv=vdudx-udvdxv2

Q: #11, find dy/dx by implicit differentiation

A: Differentiate question 11

Q: Find y''' (3rd derivative) of y = sin^2 (tan(6e^x))

A: Here,              We have given a function and we have to find its 3rd derivative.         So , the…

Q: What is the derivative of ln(sin x + cos x)

A: Consider the given function:

Q: if u=X- CoSX and V=X+ CosX find the derivative du

A: We have to use properties of derivative.

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

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Q: implicit derivative to find dy/dx of    xy + arcsin(y)+2^y=ln(x)

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

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

Q: 7 dy if Use implicit differentiation to find 8. dx dy dx +

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Q: The nth derivative of y = sinx cosx

A: We know that,  2sinxcosx=sin2x Therefore, y=sinxcosxy=122sinxcosxy=12sin2x              ⋯⋯1…

Q: FInd the derivative of f(x) =ln 1+ex/1-ex

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Q: Find the derivative. Simplify where possible. y = x tanh-lx + In /1 – x²

A: We have to find

Q: Find the derivative of y= sin cos (tan ax)

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Q: Find the equation of the tangent line to the curve y = ln(4 ln x) at the point where x = e. %3D

A: It can be solved using differentiation.

Q: Compute the derivative ln(ex+1) / 2x+1

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Q: Find the derivative of the function f(x) = (3+arctanx)^(ln(x^2 +1))

A: Apply exponent rule:

Q: find implicit derivative dy/dx of x2sin2(y)+2x2=y

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Q: Find the derivative of: sin sin(2x) sin sin(x) + cos (2x) cos(x) ans: -sinx solution?

A: We will use the formula cosA*cosB+sinA*sinB= cos(A-B) , with A=2x and B=x and simplify.

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

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Q: is the derivative of In

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Q: derivative

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Q: second order derivative of (5 sin 3x+cos^2 (3x )) is *

A: The function: y=5 sin3x+cos23x

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: calculate the derivative y = sinh(ln x)

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Q: 2. Calculate the derivative of y = arccos(e arcsin(x2)

A: Let u=arcacos(e^x) and v=arcsin(x^2), then y=u/v

Q: What is difference between the derivative of log(sin(x)) and the derivative of ln(sin(x))?

A: The difference between ln and log is the base of ln is e and the base of log is 10

Q: Solve the first and second derivative of y = cosh2x+ sinhx

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