4. Compute the derivative of f(x) in each part. (a) f(x) = sin(ev) (b) f(x) = (tan r)", x € (0, 7/2) (Hint: Use logarithmic differentiation). %3D

Q: f(x) = acos(b\x) x2 COS

A:

Q: B- The derivative is y = ln (sec (In 0))

A: Solution ) y = ln (sec(ln θ)) Using chain rule  dy/dθ = (ln m/dm) × (dm/dn ) × (dn/dθ ) m = sec(ln θ…

Q: 2. Compute the derivative of the following functions: 1-e-* (a) f(x) = V1 – sin³ x, (b) f(x) =

A:

Q: 3) Use logarithmic differentiation to find the derivative of the function a) y = Vxe&*x? + 1)"

A: Answer

Q: Find the derivative of the function. 1 In(1 + 49x 14 y = x arctan 7x dy

A: Given y = xtan-1(7x) -114ln(1+49x2)dydx = d xtan-1(7x) -114ln(1+49x2)dxdydx =…

Q: Find the derivative of y with respect to x. y = In (tan 1(5x)) dy dx

A:

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

A:

Q: Find the derivative. h(x) = In(cosh(7x)) h'(x) =

A:

Q: 3. Find the derivative of the function. y = In(t2) – arctan(-

A:

Q: What is the derivative of x sin(x) at the point (6,5)? 2 O 1 O-1 O None of the above

A:

Q: dy Find the derivative of the function x4 In 3y = y sin 3x + eta.

A: We have to solve the problem

Q: 7. Compute the derivative of y = tan-(Kr) 1. at the point r = K

A:

Q: A// Find the derivative of y with respect to x 5) 3tan-1x + sin-1x = 4 6) y = ln- 1+ ex = la,

A:

Q: Compute the high-accuracy central difference approximation for the first derivative of y = cos x at…

A: There are three types of approximations to the derivative of a function f(x) at a point a. They are…

Q: Find the derivative of the function. sin(x) y = In(1 + 6v) dv cos(x)

A: Find the derivative of the following function

Q: Find the derivative of y with respect to the independent variable. x2 y =log 8 Sx+1 1 8x+1 O In8 x2…

A:

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

A:

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

A:

Q: The derivative of the function 3+ln x is: y = cos(In x)

A: y=3+ln(x)cos(ln(x)Differentiate w.r.t.xApply the Quotient Rule:  fg'=f…

Q: find the derivative of y with respect to x, t, or u,as appropriate. y = 1 + ln t/1 - ln t

A: The given function is y=1+ln t1-ln t

Q: Consider the derivative function h (x) = -sec? (x) + 9. What is the general antiderivative of h?

A:

Q: Find the derivative of y=ln(cos(z))

A:

Q: (3) Compute the derivative of the function e2t cos tdt.

A:

Q: What is the derivative of * In(xy) = e"y – arccos(xy)?

A: We differentiate given equation

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

A: The given equation,

Q: What is the first derivative of the expression (xy)^x = e? Hint: this involves implicit…

A:

Q: Find the derivative of y with respect to x, and 0 as appropriate: y = 6(sin (In 6) + cos (In 6) а.)

A: Given equation is: y=θsinlnθ+coslnθ Differentiate each term of y with respect to θ:…

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

A: Given,

Q: Give the derivative of f(x) arctan an(e³*) at the point where x = 0.

A:

Q: Compute the derivative of h(sin x) at x = , assuming that h' (0.5) = 10.

A:

Q: If y- sin x and yn) means "nth derivative of y with respect to x", what is the smallest posilive…

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Q: If y = cos x, then the nth derivative of y with respect to x is equal to itself if n is a natural…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: What is the derivative of: y = x ln cos x

A: The given function is   y = x ln cos x

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

A:

Q: 1. Find the derivative of the function:F(x)= [ (Vt arctan t)dt .

A:

Q: 1. y = cos2(2x − 1)

A: " Since you have asked multiple question, we will solve the first question for you. If you want any…

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

A: Given:

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

A:

Q: 8. Find the derivative of the function (t)= 3sin(arccost)

A:

Q: Find the derivative of f (x) =arcoth (e³" ).

A:

Q: c. Find the derivative of y =+- et x3 cOS X 2

A:

Q: 1. Find the derivative of g(x): Int dt 1+t Cos

A: This will solve by Leibnitz theorem

Q: The derivative of: y =0(sin (In (0)))+cos(In (0 )) is:

A: Given :y=θ(sin(ln θ))+ cos ln θ dydθ=θcos ln θθ+sin ln θ-sin  lnθ θ      =cos ln θ+sin ln θ-sin  lnθ…

Q: Suppose x6 e-5y = In (xy). Find Y by implicit differentiation. dx

A:

Q: Compute the derivative of h(sin(x)) at æ = 1/6, assuming h'(0.5) 4: %3D

A: As we know that; The Chain Rule: fgx'=f'gx·g'x Let, hfx=hsinx

Q: dy Y= x ²x-> メ =人

A:

Q: V=ln( cosn 92) %3D

A:

Q: Use logarithmic differentiation to find the derivative of y with respect to x. y = ( In (3x))n (9×)…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.