S, f(x)dx = 20! ve F(0) = 18! ise F(7) =? %3D A) 20! – 18! B) 20! + 18! C) 0 D) 20! E) 8!

Q: 1. If f(x) cos(t) dt, then f'(x) =

A:

Q: Find the derivative of y given that y= x In x to ex A None of the given choices 1-In x-x In x B ex…

A: We can find the answer as below.

Q: 41. What is the derivative of f(x) = secx + 3 csc x? A. f¹(x) = sec xtanx + 3cscx cotx 3cscx tanx C.…

A:

Q: The derivative of the function y = (10e* – 10x*)(tan x) is: a. y' = (e* – 40x3) tan x + (10e* –…

A:

Q: 16. What is the derivative of f (x) = e8x+3? %3D a. f'(x) = e8 b. f'(x) = 3e8x c. f'(x) = 8e d.…

A:

Q: If the derivative of y = f(x) at x = 2 is equal to " (0 " then y = f(x) is not continuous at r = 2.…

A:

Q: 5. Why does it make graphical sense that the derivative of aconstant is zero? That the derivative of…

A: Derivative of a function is a slope of function on given point, or derivative is a rate of change of…

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 the function. 3 In (x +8) 5-5x O A. dy %3D dx (x + 8)(5 – 5x)? О в. dy 15 -…

A: Given query is to find the derivative of the expression.

Q: 3. Suppose the function f has second derivative f"(x) = x2(x – 3)(x+2)*(? – 1). = T- (a) How many…

A:

Q: Q-2) Prove that converting the Higher-Order derivatives to the finite difference formula would be:…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: 7. Let f(x + iy) = (3x²y – y³) + i(3xy² – x³). Decide if f (x + iy) is differentiable and if it is,…

A: Given function is  fx+iy=3x2y-y3+i3xy2-x3                       (i) The function f is differentiable…

Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: x=0 is near a=0.11

Q: question 32

A: Given,

Q: -10 For f(x) = 2x-3 show that f'(x) = e using the limit definition of the derivative. ind the…

A: (a) f(x)=52x-3 f'(x)=limt→xf(t)-f(x)t-x        =limt→x52t-3-52x-3t-x…

Q: 9. Suppose for sume funchion f we have its derivative, f'x) = e*sin(x), on the %3D interval o< x<…

A: We can use application of derivative in order to solve the given problem.

Q: Find the derivative of f(x) = log, (x° + x – 1). %3D 2 + x - 1 f (2) = %3D (3z* + 1) (In 2) (3z +1)…

A: Given:     fx=log2x3+x-1

Q: Compute the second derivative of  f(x)=ex+x  at x = 2 using a step size h = 0.2  The backward…

A: According to the question; f(x)=ex+x                                                     ; x=2step…

Q: 6-Iff is a continuous at x=c, then f has a derivative at x=c. * a. True b. False

A: Consider the given statement "If f is a continuous at x = c, then f has a derivative at x = c".

Q: 1. (x*+2x)°(6x²+4)dx 2. [3x²+2x+1 dx 3. (x?)/(x³-4) dx 4. (x+1)/(\x²+2x+1) dx

A: As per the guidelines we can solve 3 problems only.

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz əz (B)If Z…

A:

Q: Define a function f : R² → R² by f 2.у 1. Show that f is differentiable on A = E R² |x > 0, y > 0}…

A: To show that the function f defined as below is differentiable on A and compute its derivative

Q: What is the first derivative of f (x) = ln n A)? 3x²+7x 5х Select the correct answer below: бх-7 O…

A: Given query is to find the derivative of the expression.

Q: Use forward and backward difference approximations of O(h) and a centered difference approximation…

A: Step:-1 Note:-  1. Forward difference approximation for first derivative f'x ≈fx+h-fxh 2. Backward…

Q: 6.) What is the derivative of f(x) = x| at x= 07 a.) r'(x) = 1 c.) f'(x) = 0 b.) f'(x) is undefined…

A:

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: 10. Find the derivative of the following function. [Hint Using Chain Rule] a) F(x) = (x³ + 4x)7 d) y…

A: The chain rule says:ddx[f(g(x))]=f'(g(x)) g'(x)=d[f(g(x))]d[g(x)]·d[g(x)]dx   Note: According to the…

Q: If f(x) is odd function, then the derivative of y =sinh (-x)) equals Select one: f'(x) O y'=- V…

A:

Q: 2. Let f(x) = x² In a + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D…

A: Given that, f(x)=x2ln x +1 To find f''(1) when h=0.2 Using second derivative formula,…

Q: Let f (x) =x. cos(x2). what is the correct result of the derivative of f with respect to x? A…

A:

Q: If f(x,y)=3 sin (2x+y)-4 cos (x-y) then the second derivative f , is a. 3 sin (2x+y)+ 4 cos (x-y) b.…

A: In the question it is asked to calculate the double derivative of the function given.

Q: Find a positive value, c, for x, thot satisfies the Mean valve Theorem for derivatives for…

A:

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)…

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Q: 3 Consider the function f(x) = 2+ 1+ (x+1)? Compute the derivative f'(x) . Determine all of the…

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Q: -2 In(x) Consider the function f(x, y) 3y

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Q: 8. Find the derivative of the f(x) = ntan x at x = " А. п B. 2 In(1) C. π In (π) D. 2 n In() E. 2n…

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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: 15. Find the linearization of f(x) = vx +1 at a = 15 and use it to find an approxima- cion to v15…

A: Given: f(x)=x+1 at a=15

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: A) Consider the function f(x) whose second derivative is f’’(x)=4x+3sin(x). If f(0)=4 and f’(0)=4,…

A: According to the guidelines in case of multiple questions, We are only allowed to do first question.…

Q: Use the definition of partial derivative of a function f(x, y) = 3x² – xy? to illustrate fi and f2 '

A:

Q: 5. Let f(x) = |cosx),x € (0,21). Determine that where the function S is differentiable, and where it…

A: Since not a particular question asked as per guidelines solution to only first question (i.e Q5) is…

Q: The general anti-derivative of the function f (x) - In(x) is given by x In( x)+ C Inx)-x+ C x In(x)…

A: The integral (anti derivative) of fx=lnx can be evaluated by using integration by parts. The…

Q: Show that the function f(z) does not admit an anti-derivative in the domain N = C\{0}. Does it admit…

A:

Q: Let f(x) = In(1 + 7 x). Find flS(0), that is the third derivative of f evaluated at 0. f(3 !3D

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Q: 268 CHAPTER 4. APPLICATIONS OF THE DERIVATIVE 38. f(x) = x In x- 2x + 3 on (0, ) 67. f(x) 39.…

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Q: Let f(x) =x. cos(x2). What is the correct result of the derivative of f with respect to x? =X•COS…

A: