54th Dorivative: fle)=2-4sin (a2)

Q: Compute the derivative of the function F (x) = L evi dt.

A:

Q: Find the derivative of the function. 5x g(x) = [¨ cos(r}]dt cosx

A: We will use Lebnitz rule to differentiate the function .

Q: Consider the function f(x)  whose second derivative is f"(x) = 10x+4sin(x) . If f(0)=2  and f'(0)=3…

A:

Q: Estimate the second derivative of f (x) = difference approach with h=O.1? 25x3 6x2 + 7x -88 at x-2,…

A:

Q: Evaluate the derivative at x = 1 for y = In ()

A: For a function f its derivative is defined as f'(x)=limh→0f(x+h)-f(x)h. For some standard functions…

Q: Find the derivative of the function. F(x) = et dt

A: The function is given as F(x)=∫xx2et4 dt. The Leibnitz rule of differentiation under the integral…

Q: The nth derivative of y = Inx is given by %3D

A:

Q: Find the derivative of the funciton F(x) = ,5t dt. F'(x) =

A:

Q: Find the derivative of the function. y= log sv7x +3 dy dx I3D

A:

Q: Use forward-difference formula to evaluate the first derivative of y = sin(x) at x = O 2√2 π -2√2 ㅠ…

A: Given that y=sinx. We have to find the first derivative of y=sinx at x=π2 using a value of h=π4 by…

Q: Obtain the derivative of the function y 4y sen (3x) – 7x In(2x + y) = e* - ey + 4tg(y)

A:

Q: What is the derivative of y = ekx? For what values of k does this rule apply?

A: Given function is, y=ekx. The derivative of the given function is found as follows: dydx=ddxekx=kekx

Q: Find the derivative of the function. 1 3x' g(x) = dt 1 + t4 Jtan x

A: Given : g(x) = ∫tanx3x211+t4dt

Q: Use forward difference approximation to estimate the first derivative of the following equation.…

A: Given that, fx=-0.15x3-0.2x2-0.5x+2.25h=0.5We need to find the first derivative of the function at…

Q: Evaluate the derivative of y = sin'6x + In /1- 36x, where x= 0.125. dx |x= 0.125 U (Type an integer…

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: Use forward and backward difference formula with h = 0.1 to approximate the derivative of f(x) =…

A:

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

A:

Q: Find the derivative of the function. 3x2 g(x) • dt 4 + t3 tan x g'(x) =

A:

Q: Find the derivative of f(x) = Vx2. What is f'(5), rounded to 3 decimal places?

A:

Q: 10. y = Jx

A: We have to find derivative of - y=f(x)=1x using delta method. Delta method to find derivative is…

Q: What is the 4th derivative at x = 0 of the function f(z) = (2r + 1)* %3D

A:

Q: Find the derivative of the function g(x)= integral  x2  tanx  (1/square root 4+t4) dt

A: Leibnitz integral rule for Differentiation :               ddx ∫α(x)β(x) f(t,x) dt = ∫α(x)β(x)…

Q: Compute the derivative of h(sinx) at x = π,/6 , assuming that h' (0.5) = 10.

A: We have to compute the derivative of function hsin x at x=π6, assuming that h'0.5=10. We know the…

Q: Find the derivative of the function. • 2x2 g(x) = 1 dt 3 + t3 /tan x g'(x) =

A:

Q: Consider f(x) = 3 − cosx on the interval [0, 7]. When will the first derivative equal zero?

A:

Q: What is the derivative of y = e3 In(5 + e3)? %3D

A:

Q: b) Use the method of Differentiation from first principle to prove that the derivative of the square…

A: Consider the provided information, ddxx=12x Prove that left hand side is equal to right hand side.…

Q: Calculate the derivative of the function below using the quotient rule. 28 y = Vx + 8x7 f(æ) = %3D…

A:

Q: Find the derivative of f(x) = 9 sinh-' (x²) – 9 In ( Vx4 + 1). %3D

A:

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

A:

Q: Find the derivative of f (x) = V7– 4x. To enter va, type sqrt(a).

A:

Q: 1 m' (x) = x In(x)

A: Given: m'x=1xlnx for finding anti-derivative of given expression, we substitute lnx=u…

Q: Use backward, forward, and centered difference approximation to estimate the second derivative of…

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: 8. y = va? + x²

A:

Q: Find the derivative of f (x) = VI- 4z. To enter va, type sqrt(a). f' (2) = 固助

A:

Q: Find the derivative of the function.

A:

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

A:

Q: Compute forward difference approximations for the first derivative of the function, y = e*cos(x²),…

A:

Q: Use Dnf (x) to approximate the derivative of f(x) = sin(x) at ;h = (0.01,0.2) 4

A: Given fx=sinx at π4, h=0.01,0.2

Q: Find the derivative of g(x) = fecost dt.

A:

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

A:

Q: What is the derivative of the function B(x)=3/(x+2) at x=a?

A:

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

A:

Q: The derivative of y = cos²x is %3D

A: Given -                  y= cos2 x . We have to find the derivative of y.

Q: Approximate the derivative of y=x² at x=1 by forming small changes

A: We have to find the derivative of the function y=x2 at x = 1 by forming the small changes.

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: Find the first derivative of the function below: f(#) = cosh(cot(z² – 2x – 7)) %3D

A: