2. Use the definition of the derivative to find f'(x) and f"(x). a) f(x) = x? %3D

Q: What is the first derivative of s(x)=(7x)3x at x=4?

A: To evaluate s'(4)

Q: Find the derivative of the function.…

A: The given function is hx=x2arctan8x

Q: Use three-point midpoint formula to evaluate the first derivative of y = cos(x) at x = 5 using a…

A: Given function is y=cosx. We have to find the first derivative of y=cosx at x=π2 using a value of…

Q: Explain the method of proving the derivative (dy/dx) of sinh(x) and cosh(x) ?

A:

Q: By using the definition of the derivative, find the for: - dx 1- f(x) = Vx

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Q: How to solve for the derivative of Dy[tan(y)+1/tan(y)-1]? If it's 0, why?

A:

Q: Find the derivative of function.

A: The given function is f(x) = ln(xex+2).We have to find the derivative of this function with respect…

Q: Find the derivative. h(x) = In(cosh(7x)) h'(x) =

A:

Q: What is the derivative of 1+x3 at the point (1, )? O 1/4 O- 1/4 O 1

A:

Q: B. By using the definition of the derivative, find the for: - dx f(x) = x -

A: Explanation of the answer is as follows

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 the derivative of the function: f (x) = (+ Inx)² а.

A:

Q: Find the derivative of y with respect to x of y = xlnx – x.

A: Using rules of differentiation.

Q: Evaluate the derivative of the function. y= sec "(2 In 8x) dx

A:

Q: 1 Find the first derivative given that f(x) = xdx +

A:

Q: Use three-point midpoint formula to evaluate the first derivative of y=tan(x) at x = O-2√/2 00…

A: Given function is y=tanx. We have to evaluate the first derivative of y=tanx at x=π4 using a value…

Q: Find the derivative of 3 In xy + sin y = x².

A:

Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 (x2)

A: Given function is y=cos-1x2. Chain rule of differentiation states that: ddxfgx=f'gx·g'x…

Q: 2. Use implicit differentiation to find the derivative of y with respect to x for the following: xe…

A:

Q: Obtain the derivative of the function y (3 sen(4x))° ( tgʻ(2x)) y = (sec(2x))* – 1

A: This question is based on Trignometric application and diffrentiation of function.

Q: Compute the second derivative with respect to x of 3x3 + 8 y = at x = 1.

A:

Q: Find the most general anti-derivative of f(x) = 9Vx +1+ cos x.

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Q: Find the derivative of y with respect te X /3 %3D

A: Finding dy/dx

Q: 4. Compute the second derivative with respect to x of 3x³ + 8 y : at x = 1.

A:

Q: find the derivative of y with respect to the appropriatevariable. y = (x2 + 1) sech (ln x)

A: Given: y=x2+1sechlnx

Q: What is the derivative of: y = ln ln(1 − cos x)

A:

Q: Give the derivative of f(x) arctan an(e³*) at the point where x = 0.

A:

Q: what is the derivative of f(x)=ln(tanhx)

A:

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

A:

Q: The derivative of y = -ln(cos(ex + 1)) is

A: Our Aim is to find the derivative of y=- ln cos ex+1 -(i)

Q: 3/ By using the definition of derivative, proof that tan x = sec? x. %3D dx

A: By definition of derivative , f'(x) = d(f(x)dx= limh→0f(x+h) - f(x)h L Hosital's Rule :When limit is…

Q: The derivative of xª at x = e is equal to .Soloot ono

A:

Q: Find the derivative. 8 + e y = In 8 + et 8 - ex.

A: Given,          y=ln8+ex8-ex

Q: 2. If f (x) = xV x + 3, find the derivative of this function and the slope of the tangent line at…

A: Product rule of differentiation: (fg)'=fg'+gf' The slope of a tangent line at (a,b) is given by:…

Q: 2. Find from first principle the derivative with respect to x of the function f(x)= Inx.

A:

Q: f(x) = x*Inx

A: TO FIND 5th order derivative f(x) = x4 lnx FORMULA USED  BIPART PRODUCT RULE OF DIFFERENTIATION…

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: The derivative of y=eSinh/x +cosh¬/x equals

A:

Q: 3. Find the derivative of: y = csch¬(In (sech(sec()))).

A: Note:Two questions submitted simultaneously, kindly upload question 2 separately.

Q: Find the derivative of y with respect to x for y=2x   ???

A: y=2x

Q: The derivative of x at X = 1 is to I Frue or false 2

A:

Q: If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.

A: Now the derivative of a function f at a point 'a' is given by,

Q: 13 Find the secord derivative cy") y= x°+3x - when

A: see below the answer submit the q12 with what to do with the question

Q: Compute the second derivative with respect to r of 3x + 8 y = at x = 1.

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Q: Obtain the derivative of the function y (ctg(5x))} y =- - sen? (5x) + 1

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Q: Find the derivative. f(x)=tanh(2 + e^3x)

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Q: Find the derivative. f(x) = tanh(2 + e4x) f '(x)

A:

Q: Use three-point midpoint formula to evaluate the first derivative of y = sin(x) at x = using a value…

A: To find- Use three-point midpoint formula to evaluate the first derivative of y = sinx at x = π2…

Q: 2 Use the definition of derivative to find the equation of line tangent to f(x) = 2 through x = 3.

A: