0 2 _y|1 3 4 6 4 9 According to the table, which of the following is the value of y'(4) calculated with the forward numerical derivative formula? O A) 1.5 O B) 2.5 О с) 0.5 OD) 4.5 OE) 3.5

Q: With respect to x, what is the derivative of: * du In(u) O Option 2 Option 4 du Option1 Option3

A: apply chain rule

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: 4. It f(x,)= (x?+Zy^)+Z and ū= a.) Find the derivative of t in the direction Of ū at 13,2) -

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

A:

Q: Find the derivative of y with respect to the independent variable. y = 9cos zO O A. - 19cos AO In 9…

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Q: 1.x3 = at?, find the second derivative of "x" with ,d²x respect to "t", 'dt2

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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: Compute backward difference approximations for the first derivative of the function, y =[ e'nxP, at…

A: We have to compute backward difference approximations for the first derivative of the function,…

Q: Find the derivative of y with respect to s. y= sec 1(7s° + 4)

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Q: Find the derivative of y with respect to 1. y = In V4x2 + 7x %3D 2. y = sec?(e-4*)

A: A detailed solution is given below.

Q: Use forward-difference formula to evaluate the first derivative of y = sin(x) at x = O 2√2 π -2√2 ㅠ…

A: Given that y=sinx. We have to find the first derivative of y=sinx at x=π2 using a value of h=π4 by…

Q: 14) The derivative of y = cscx sin x is y = 0 A) True B) False

A:

Q: Find the derivative of h(z)=(az+b)/q  . Assume that a, b and q are constants. h′(z)=

A: Given function is, h(z)=(az+b)q where a, b & q are constants.

Q: Compute backward difference approximations for the first derivative of the function, y = e*cos(x?),…

A: We have to compute backward difference approximation for the first derivative of the function,…

Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1,1) in the direction of from the…

A: We have to find the directional derivative.

Q: find the first order derivative of y=sin 0.5√x/x at x=8, h=0.2 a. Forward difference B. Backward…

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

A: We differentiate given equation

Q: Compute the derivative of h(sinx) at x = π,/6 , assuming that h' (0.5) = 10.

A: We have to compute the derivative of function hsin x at x=π6, assuming that h'0.5=10. We know the…

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: In Exercises -. , find the derivative of y with respect to the appro- priate variable. 37. y = sV1 –…

A: Since, you have asked multiple questions we will answer the first one for you. If you want any…

Q: Compute backward difference approximations of O(h), for the first derivative of y = cos x at x =…

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Q: What is the derivative of y = e3 In(5 + e3)? %3D

A:

Q: What is the first derivative of y=tanh(0³+30)? A y'=3(0²+1)sech (0²+30) dy =3(0²+ 1)sech²(0²+ 30) B…

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Q: (§5.5, Q34) Calculate the derivative d dæ ), Vi dt.

A:

Q: Compute backward difference approximations for the first derivative of the function, y = cos(sin(x)+…

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Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

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

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

A: Given,

Q: Birinci mertebeden geri yön sayısai Ay O a) y': h Vy O B) y'= O NS) Vy y'= h

A:

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

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Q: If u, v, w are nonzero differentiable functions, then the first derivative of uv / w is

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Q: a*+1 +1 t4 +1 dt with respect to x. Calculate the derivative ol Jsin(x)

A:

Q: 3. Use the forward-difference formula to approximate the derivative of f (x)=sin(In x) at x, = 2.5…

A: The derivative of the function can be calculated using the difference method. The formula for the…

Q: Compute central difference approximations for the first derivative of the function, y =[ elnx)2 , at…

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Q: Calculate the derivative of y with respect to x, if x³/2 + y¯3/2 =7. dy dx

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Q: The derivative of the function y 1 = COS Va at a = 0 is equal to

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Q: Compute the high-accuracy central difference approximation for the first derivative of the function…

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Q: 2. Please find the derivative of the following: S* cos vt dt J. cos b. Scos VE dt a.

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Q: Compute the derivative of g(x) = cos(t²) dt. O 42 sin(z*) O cos(x*) -42 sin(z*) O 4a cos(a) O -…

A:

Q: Compute forward difference approximations for the first derivative of the function, y = cos(sin(x)+…

A: Given is the function  y=cos(sin(x))+1) Forward difference is found as:F'xi=Fxi+1-FxiΔx

Q: 2- Find the derivative of y with respect to the Exercises 1-3. y 1- 6 sinh || 1 y sinh (2x + 1) 2-…

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Q: Let y be defined implicitly by the following equation as a function of x and z : eyz +sin(tyz) – xyz…

A:

Q: Compute forward difference approximations for the first derivative of the function, y = e*cos(x²),…

A:

Q: 2- Find the derivative of y with respect to the Exercises 1-3. = 6 sinh 1- 1 sinh (2x + 1) 2- In…

A: These are the hyperbolic function so use standard form of derivative of hyperbolic functions.

Q: 5. Compute the derivative, r'(t), of r(t) = (et-4, t, In(1 – t)).

A:

Q: 2) Find second derivative d'F/dt? of 312-2 F? = 13 and find it at (t,F) = (-1,2)

A: We have to find the required second derivative at the given point.

Q: Compute the first, second, and third derivatives of r(t) = 9ti + 5 In(t)j + 5e-3tk. first derivative…

A: As we know that; The Sum/Difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 The Chain rule:…

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: V=ln( cosn 92) %3D

A:

Q: Example2: Find the derivative of w=xy+z if x=cos t ,y=sin t &z=2t?

A: