7.2 Use appropriate method of differentiation to determine the derivative of the following functions (simplify your answers as far as possible). 3V5 - 2ve" (a) t(v) = (b) f(z) = In (r+ In z) (c) h(z) = Vre²-² (z+1)

Q: 1. Find derivative of given function defined as follows. 7-29-22 y = (8x²-3x³) ³

A:

Q: 2. Calculate the derivative of the following y= (*- 3 + Sx) B. Ytan (x+ Se-2) (4x + 3) Tx-2) A. C.…

A:

Q: 1) Find the derivative of the given function with respects to e 3tan ở In 3 y

A: Given

Q: 2. g'(x) where g(x)= x² +7x-5

A: differentiation by using first principle

Q: 4) Calculate the first derivative of the following functions: 1. f(x) = In 2x2+1° 2. f(x) =…

A:

Q: 15. Which of the following has terminating derivative? 1 1. у %3 Зх3 — 2x2 + х-1 —5 II. y Зx+2 1 . у…

A: We will find the terminating derivative.

Q: 1. Determine the first derivative of the functions below with the rules for deriving the function:…

A: A Given function is y=4x3+32. Use formula ddxxn=nxn−1 Differentiate  y=4x3+32 by using the chain…

Q: 4. Find the derivatives with respect to x of the function 2 – 3x^2. 5. Differentiate ax² + b to the…

A: Using derivative of composite function.

Q: Find the derivative of the function. f(t)= cosh2 (2f2 + 9) 8t cosh (22 + 9) sinh (22 + 9) b.8t sinh…

A:

Q: Calculate the second and the third derivative of y =ar y" -(8/(pix^5)) -(48/(nix^7))

A:

Q: 1. Use the definition of the derivative to find the derivative of the following functions. 1 (b)…

A: use definition of derivative to find the derivative of the following functions a) fx=x+2 it is known…

Q: Determine the derivative of the following functions. 1. у 3 (8ӕ — 1) sinh(8a — 1) 2. y = (5)…

A:

Q: 6. Determine the derivative of the following functions. Do not simplify. (a) y = 2t° +t+ e² 2 (b) y…

A: Given:           (a) y=2t5+t+e2Differentiating with respect to…

Q: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 1. Use forward and centered difference approximation method to estimate the derivative of the…

A: Given that, the function is fx=x3-2x+4 and x=1.75, the step size is h=0.25. "Note that,  The forward…

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: Compute the derivative of the following: 3 +. 2.1x 5 g(x) =, 4.

A:

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: Compute forward difference approximations for the first derivative of the function, y =[ eln(x)2, at…

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Q: Find the derivative of the below functions: In(x) y = 1-8 In (x) y' = (a) = In(/ 5x – 7) y = INV5X -…

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Q: Find the derivative of the function. (3x +5) f(x) = In (7x + 5)*(2x+ 8) 14 2 O a. 3x +5 + 7x +5 2x…

A: We have to check

Q: 3. Find the derivative of y with respect to x in the following functions : 18x'y (ans.: (3x-2) a)…

A:

Q: 4. Find the second derivative for the following functions: a) (ans.:6x +

A: Derivatives

Q: What is the derivative of the expression (xy)" = e 1+ In(xy) 1+ In(xy) y O Option 1 Option 2 1+…

A: Given (xy)x=eTo find Derivative:

Q: OFind the derivative of the 1 +5 (a). f(z) = %3D T2-5

A: As per the guidelines we can solve only one question at a time so if you need more answers then…

Q: question 31

A: Consider the given function.

Q: 2. What is the equation of the tangent line to the curve y = x? - 2x +1 at point (3,4)? а. у3 2x — 2…

A: The equation of line is y-y1=mx-x1, where m is the slope of the curve.

Q: Find the derivative of the following using the three-step rule Зх — 1 1. y= 2х+5 2. y=Va? +x?

A:

Q: Physicists sometimes have to compute derivatives of the following form: (1) o2 – 1 do do Use the…

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Q: 3 Suppose 8 (x): 2(1- 5x)3 .What is the correct result of the derivative of g with respect to x? 45…

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

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Q: 4. Find the second derivative of each of the following and determine based on your results if the…

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

A:

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

A:

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

A:

Q: 1. Use forward and centered difference approximation method to estimate the derivative of the…

A: Given the function is fx=x3-2x+4. The forward and centered difference approximations to estimate the…

Q: 1. Use the definition of derivative to find f'(1) 2r2 b) f(x) = Vx

A: Derivative of the function using definition

Q: 6. у3 In (x*+3х -1)2 V(5x+2) step1 step2

A: Derivative of function

Q: -7/2 = 8. Calculate the derivative of y with respect to , if x/2 + y dy dx

A:

Q: What is the first derivative of s(x)=(7x)3x at x=4? Select the correct answer below:…

A: As s(x)=(7x)3x The function can be rewritten as:s(x)=x3x. 73xIts first derivative is given by the…

Q: 5. (a) Use the limit definition of the derivative to find the derivative of f(x) = V5x +1. V5yl th)-…

A: Given; f(x)=√(5x+1)

Q: 2. Find the derivative of h with respect to u if h = n²u

A:

Q: 11. 5 4 Determine the derivative of y=x° – x* + 6. - Enter your next step here dy ab a + JT 00 () dx…

A:

Q: Compute the derivative of the function f(x) = S7+3x²' at the point 4, using the definition. Ex. 2.…

A: Derivative.

Q: 2. Determine the true error and the relative true error of the first derivative of f(x) = 2.5-* %3D…

A: Solution is below

Q: Зх +1 a) y =- 1 b) g(x)= Jx -

A:

Q: 2-х Find the derivative of y = Зx+1 -7 бх-5 6- А. (3х+1)2 В. (3x+1)2 7-6х С. (3x+1)2 D. (3x+1)2 Е.…

A: Proceed as shown below

Q: Find the derivative of the following functions by applying "Delta Metho Show your complete solution.…

A:

Q: 19. What is the seсond derivative of y бх* - 3x1 + х2 -57 а. у 24х1 — 9х2 + 2х b. у"3 144х — 18 с.…

A:

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.