Differentiate the function In e* 8.) y = ex 7.) f(x) = e** – In :

Q: Use the definition to calculate the derivative of the criterion of the function f(x) = e14x. In…

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Q: Use the Cauchy Integral Formula for Derivatives to compute

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Q: give 3 examples of the reciprocal rule of integration formula

A: The reciprocal rule for the integration is: ∫f'(x)f(x)dx=ln |f(x)|+C

Q: Give a vector valued function whose graph is same as y=ln (x)

A: We know that a function with the representation r→t=ft i∧+gt j∧ is called a vector valued function…

Q: calculate the required derivative using the chain rule. -1 Z=tan tan () » yorsinə u =Y Cose %3D az.?…

A: We use chain rule and quotient rule

Q: Find the derivative of O2 sec 2x O 2tan 2x O-2 cot2x O 1/cos2x y=In sin 2x

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Q: verify the statement by showing that the derivative of the rightside equals the integrand on the…

A: Given statement :

Q: Use implicit differentiation to find * az given that yz* + x²z3 = дх = exyz

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Q: Use linear approximation or differentials to estimate the following

A: Solution: Consider the given number: 1000.033 Let y = x3 = x13 Differentiating with respect to x:…

Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

A: To calculate the integral

Q: Consider f(x, y) =(ax² + by²). Based on the second derivative test, what are the conditions…

A: Answer

Q: Use Leibniz’s Rule to find the derivatives of the functions

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Q: 3. The derivative of /(x) = In x at x = 3 when hourrent = 0.001 and hprevious = 0.002

A: Given problem:- 3. The derivative of f(x) = In x at x = 3 when hcureent= 0.001 and hprevious = 0.002…

Q: п-(х-4)" 22и. (2n — 1) Ax) =En=0 n:

A: Solution of given problem as follow

Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

A: We write the expression using exponent and then integrate C=integrating constant

Q: 2. Calculate the first derivative of f using the forward and backward difference approach in the…

A: The objective is to calculate the first derivative of f using the forward and backward difference…

Q: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

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Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

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Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

Q: Find the tangent line to the function f(x) = 2x cos4(x) at the point (0,1)

A: We have given function fx=2xcos4x and point 0,1. We have to find tangent line to the function at the…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of f(x) = Lret dt Sainx %3D

A: Using the fundamental theorem of calculus to find the derivative of: fx=∫sinx7et2 dt Solution:…

Q: Find the derivative us ing the defini tion O fx). %3D

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Q: The length and width of a rectangle are measured as 25 cm and 36 cm, respectively, with an error in…

A: Given length of a rectangle, l =25 cm           Width of a rectangle, w=36 cm We know that,  Area of…

Q: To compute fxyz, we first take the partial derivative with respect to which variable?

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Q: complete solution

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Q: Is the functionf(x) = |x| cosx differentiable at the point x =0 ? (Use definition of the derivative)…

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Q: 7) Use a tangent line approximation with the function g(x)= Jx to estimate 9.2 . %3D

A: topic - tangent line approximation note :as per bartleby guidelines we are supposed to answer only…

Q: Compute the derivative of g(x) = | 1 dt. 2 1+t5 2" 1+æ15 1+25z 2" In 2 1+æ15 1+25z 2" 1+a15 1+25z 2"…

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Q: Use a linear approximation (or differentials) to estimate the given number.   27.tan 2°

A: The Linear approximation of the function at x=a is given by L(x)=f(a)+f'(a)(x-a) To Find Linear…

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

A: We have to verify that given statement.

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: Find the derivativeof the following function:

A: To determine derivative of the function.

Q: Estimate approximate derivative of f(x) = x2 at x = 1, for h = 0.2, 0.2, 0.05, 0.01 using first…

A: Given function is fx=x2. We have to estimate approximate derivative of the given function at x=1 for…

Q: What

A: The correct option is (B).

Q: 16. r(0) = sec 0 tan 0 – 2eº -

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Q: Show that the function has partial derivative at the point (0,0) but is discontinuous at this point.

A: solve the following

Q: Use differentials to approximate the value of s2.1. O 100+6ln5 4 O 50+5ln5 2. O 100+5ln5 4. O…

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Q: Exercise 18 Get the second derivative of the function f(x) = e3en el point 1.3 Using Richardson's…

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Q: what is the maximum value of y=sinx, 0 less than or equal to x less than or equal to 2pie, and…

A: Given function  y = sinx on  0≤x≤2π

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

A: NOTE: Refresh your page if you can't see any equations. . on the right-hand side, we have

Q: Find the fourth derivative of f (z) = 3* + In (z) – 191z. Enclose arguments of functions in…

A: To find :  Fourth derivative of function ,  f(x)=3x+lnx-191x

Q: Find the orthogonal trajectories of family of curves y = ax5 (SOLVE BY USING DIFFERENTIAL…

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Q: Q Find the derivative us ing the de fini tion 2. O fcx) Fcx) x+2X %3D

A: Derivative of the function using definition

Q: Use linear approximation or differentials to estimate v80. Show your work.

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

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Q: Find 1" and 2nd order partial derivative for the function ax²+by²+2hxy and also verify дхду дудх

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Q: s(w) = In( w - %3D

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Q: (In iny

A: To find the derivative of the given function- lny=lnxylny Here we will use the following formulas-…

Q: 2.) Investigate the derivate of the function f(z)=Imz by using definiton of derivative.

A: The derivative of a function is represented as the change in variable with respect to change in…