6. Find the first order derivative with respect to z of the function u = In/x2 + y2 +z²

Q: Find derivative of the function f(z) = (sin¬' (2z – 1))² with respect to z.

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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: The derivative of f(r, y) at P(1,2) in th in the direction of-2j is -3. Then the of -i - 2j is

A: It is given that the directional derivative of f(x,y)  at P0(1,2) in the direction of (i+j) is = 22…

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

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Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

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: 4. [ ]Find the derivative of y with respect to the given independent variable: Ins 7x (a) ex³y = 2x…

A: Given equation ex2y=2x+2y   As per our guideline, we  supposed to answer only the first three…

Q: Find the partial derivative of the given In[y? sec(x²y²)].

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Q: 1. Compute forward approximations of O(h) and O(h² for the first derivative of y = e* evaluated at x…

A: 1st we will derive formula for O(h) and O(h2) and then find corresponding values

Q: Find the derivative of y with respect to x. y = 8 In (4 In x) dy dx II

A: Topic:- derivatives

Q: Find the derivative of y with respect to X, t, or 0, as appropriate. Inx y=5

A: Given: y=ln xx5 So, the derivative of y with respect to x is: dydx=ddxln xx5 According to the…

Q: 2. Calculate the derivative of the following. А. y = (x* – 3x² + 5x) ³ DUKAS B. y = tan²(x² + 5x –…

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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: 10) Find the second derivative of k(z) = 4 cscz.

A: Given: kz=4cosecz for finding second derivative of given function, we find first derivative then…

Q: What is the derivative of (6 x+1)5 (4 x-21)16 (21 x-23)3 (3 x+25)4 y = In with respect to x?…

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Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

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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: In(x), Sn (4t + et) dt. Find the derivative of F(x). 3.

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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: (e) Use a backward finite difference approximation to approximate the first derivative of the…

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Q: . Compute the central difference approximations of O (h^4) for the first derivative of y = cos(x) +…

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Q: Use forward, backward and central difference approximations to estimate the first derivative of:…

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Q: If we are getting the partial derivative of f(x,y) with respect to x, we are letting the y variable…

A: hello greetings from bartelby.i am here to help you.

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

A: On simplification, we get

Q: Shows the derivative function of: u³ + 2u, where u = x² + 3

A: Let's find.

Q: Find the derivative of y with respect to the appropriate variable. y= cosh 2x+2 O A. V(4x + 9)(x +…

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Q: Find the weak derivative of f() = |x² – x + 1/5| on the 1) interval (0,1).

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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: 3. Calculate the derivative of f(x) = tan(4t) dt. %3D -1/16

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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: 2. Prove from the definition of derivative that for n EZ, d ng"-1 dr

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Q: 2. Show that the function psin(2r) e-*dt g(x) = is differentiable on R and compute its derivative.

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Q: 4. Show in two ways that the function f(z) = exp(z²2) is entire. What is its derivative? Ans. f'(z)…

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

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Q: Y= In (In2 (1-x))re?

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Q: Find the derivative of F(x)

A: To Determine: find the derivative of F(x) Given: we have Fx=∫2x3costdt Explanation: we have a…

Q: 5. What is the value of the second-order derivative of the function with parametric expression x =…

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Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: Evaluate the 3rd derivative of M with respect to (x) M= x6 y3 Cos (x6 y3) if x =6 and y= 3

A: The function is M=x6y3cosx6y3. Using implicit differentiation, find dydx.…

Q: Find the derivative of y with respect to x. 6 y = (x³ In x) %3D dy dx II

A: Please see the below picture for detailed solution.

Q: 15 - What is the approximate derivative of f(x) = 5x³ + 4x² if we use f(ze+h)–f(za) forward…

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Q: (e) Use a backward finite difference approximation to approximate the first derivative of the…

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Q: Find the fourth derivative of f (z) = 27 + In (z) – 160z. %3D

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

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

A: This will solve by Leibnitz theorem

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: Зх +1 a) y =- 1 b) g(x)= Jx -

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

A: