Suppose that the values of a smooth function fis known for x=0, 0.3, 0.6 and 1.2. Select the 3- point numerical differentiation scheme that will best approximate f'(0.6).

Q: Suppose that the values of a smooth function fis known for x-0, 0.3, 1.2, 1.5 and 1.8. Select the 3…

A: Three point forward difference formula for finding f'(x) with step size h is given by,…

Q: Suppose that the values of a smooth function fis known for x=0, 0.3, 1.2, 1.5 and 1.8. Select the 3…

A: Forward difference numerical differentiation will be used.

Q: compute the derivative. g(x) = tanh−1(ex )

A: We have to compute the derivative of the function: gx=tanh-1 ex We know the formula of derivatives,…

Q: Find the equation of the tangent line to the graph of y at (2, 금). Use the limit process in finding…

A:

Q: Suppose that the values of a smooth function fis known for x=0,0.3, 1.2, 1.5 and 1.8. Select the 3…

A: Given f is  a smooth function. Value known for x=0, 0.3, 1.2, 1.5 and 1.8 We have to select the…

Q: Which order of differentiation will calculate fxy faster: x first or y first?  a. ƒ(x, y) = x sin y…

A: The given function is,

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

A:

Q: Determine the intervals along the x-axis on which the derivative in Figure 16 is positive. y 4.0 3.5…

A:

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

A: We will do all three parts.

Q: By using first principle of differentiation find f'(y), if ƒ(y) = Му—N

A: Given: f(y)= My-N According to the first principle of differentiation, the derivative of a function…

Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 x - x sech-1 x

A:

Q: - Use the definition of derivative to find the tangent and normal equations of f(x) = (x - 3)2 %3D…

A: We can find the tangent equation and normal equation as below.

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 y with respect to the appropriatevariable. y = (1 - θ) tanh-1 θ

A: Consider the following equation:

Q: Find the critical points/number of the function h(x) = e^x sinx-sinx+cosx by applying derivatives.

A: First calculate its derivate then equate it equal to 0 to obtain the critical points. h(x)=exsin…

Q: Use the First Derivative Test to find the relative extrema of ƒ(x)=· sin x on (0,27).

A: The given function is- fx=x2-sinx  Differentiating f(x) w.r.t x- f'x=12-cosx Put f'x=0,…

Q: Suppose that the values of a smooth functionfis known for x-0,0.3, 1.2, 1.5 and 1.8. Select the 3…

A:

Q: Which order of differentiation enables one to calculate fxy faster:x first or y first? Try to answer…

A: Given function is fx,y=xsiny+ey. Partial derivatives are derivatives of multivariate functions taken…

Q: Determine the derivative of the following functions. 1. y = tanh (8x – 3) 2. y = 2x sinh(6x – 5)

A: Here we will use standard formulas for derivative of inverse hyperbolic functions, product rule of…

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

A:

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 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: Find the derivative of the function by the limit process. h(s) = −2 (square root of x)

A:

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

A:

Q: Suppose that the values of a smooth function fis known for x=0, 0.3, 1.2, 1.5 and 1.8. Select the 3…

A:

Q: Use forward, backward and central difference to estimate the first derivative of f(x) = In(x) at x =…

A:

Q: Compute backward difference approximations for the first derivative of the function, y = log(x? +…

A: Given is the function y=log(x2+1)2   .  It is needed to compute backward difference approximation…

Q: fcx)= Y文 メ ー^

A: Local extrema

Q: compute the derivative g(x) = tanh−1(ex )

A:

Q: Find the equation of the tangent line to the curve at the given point using implicit…

A: Given equation of curve is (x2+y2-y)2=x2+y2 Differentiate both sides with respect to x.…

Q: (6) Find the derivative where it exists (c) Where is flz) analytic ?

A:

Q: Find the derivative of the following functions using the long method (limits) y= tan x

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the derivative of Vry = -3+x*y° using implicit differentiation.

A:

Q: show that the function is derivable and that the derivative is continuous.

A: The objective is to show that the given function is derivable and the derivative is continuous.…

Q: Derive a formula that approximates the second derivative of the function sampled at x = 0, 0.01,…

A: Let us assume that second derivative function  f"x0=Afx0+Bfx0-h+Cfx0+2h can be rewritten as…

Q: Shows that if a function f(x) is continuous in interval [a,b] then most likely the derivative of…

A:

Q: Apply central divided difference approximation (CDD) to find the first 5 derivative of F(x) = e0.8x…

A: To find the first five derivatives of fx=e0.8x when x=24 using central divided difference…

Q: find the derivative of y with respect to the appropriatevariable. y = sec-1 (2s + 1)

A: The given function is y=sec-12s+1.

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: Use Richardson extrapolation to estimate the first derivative of Y = sin x at * = π/4 using step…

A: Given the function  y=sinx

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

A:

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: Use high-accuracy differentiation formula O(h) to estimate the first derivative of f(x)=log.x.…

A: Consider the given function, fx=logx Here we need to estimate the first derivative of the given…

Q: Use Richardson extrapolation to estimate the first derivative of y = cos x at x = π/ 4 using step…

A:

Q: 1. y = cos2(2x − 1)

A: " Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Differentiate the given by implicit differentiation x3 - xy + y3 =1

A:

Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Given: fx=xx+1 We want to find a linearization at a suitably chosen integer near a at which the…

Q: A function at x=2.1 , 2.2 , 2.3 has values 22, 18 , 16 respectively . the most accurate first…

A: the values f(2.1)=22,f(2.2)=18 and f(2.3)=16 the derivative…

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.