Given the function f(x)= 2 sin(3x), approximate it's first derivative at x-0.4 using equally spaced data from 0.3 to 0.5 using the following: NOTE: use 4 decimals for your calculations

Q: Find the derivative f'(x) of the following function f(x). f(x) = sinh (x + 8x*)

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: 9)/6)= (2x+1)*

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: Find the actual error when the first derivative of f(x) = sin(2x) at x = 1/8 is approximated by the…

A:

Q: find the derivative of y with respect to the appropriatevariable. y = sin-1 3/t2

A: We differentiate with respect to t using chain rule.

Q: Find the derivative of the following function with respect to x. /5x + 8 1 – 9 cos (4.x) - h (x) =…

A: The given function is:hx=5x+8 1-9cos4x3x2+10x4 This function can be written as: hx=5x+812…

Q: 2. x² + 4xy + y² = 1

A: Differentiation

Q: For the given function, find the first derivative f' f(x) = e* · (3 sin x + cos x) + 4x3

A: Differentiate both sides of the equation, with respect to x using the product rule of derivative to…

Q: Find the first derivative of y with respect to x (y') of the given function using rules for…

A:

Q: Find the approximate value of derivative f(0) with the step size h for the following function by…

A: The three point end point formula with error is where h is the step size. If the step size is…

Q: (c) Find the derivative of nh (cosu). Where n is 482

A:

Q: Use the General Power Rule where appropriate to find the derivative of the following functions.

A: Given, st=cos 2t

Q: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

A: y=ex2+1 sinx3

Q: Compute the derivative of the following function and find its tangent line at x = 0. Graph the…

A:

Q: h(x)= cot r11- tan"x

A: Given, hx=cot-11x-tan-1x We have to find h'x.

Q: 1. sin(x + y) = xy² – 2x3

A: Given- sinx+y=xy2-2x3 To find- The derivative of the above expression using the implict…

Q: Calculate the derivative with respect to x of the other variables 22) sin(xt)=t

A:

Q: s(x) = e" ln(x)+ sec(x)

A:

Q: Find the derivative of the following function. (3x² – 5) y = Cos z + (x² + 1)0* sin 5x

A: Given  y = 3x2-55sin5x + x2+1cosx

Q: Find the second derivative for the functions defined as follows .p(x) = sin(x2)

A: We have to find second derivative of the function: px=sinx2 We know the formula of differentiation,…

Q: Find the derivative of the following function with respect to x x = sinh2y

A:

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

A:

Q: Find of the function given implicitly and evaluate the derivative at the given point. y = sin ( 8x+…

A:

Q: find the derivative of y with respect to the givenindependent variable. y = log2 r . log4r

A: Recall the properties of logarithms:

Q: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

A: Using the quotient rule.The formula is-ddt[f(t)g(t)]=g(t)ddtf(t)-f(t)ddtg(t)[g(t)]2…

Q: find the second derivative and simplify the final result 7. y= Arccos(e^2x)

A: To find     d2arccos(e2x)dx2

Q: Find the derivative of the given function. y = x² sin 'x+x cos 4x

A: For     y=fx gx    dydx=fx ddxgx+gxddxfx   This is the multiplication rule of derivative .

Q: Find the derivative of the given function f(0) = sin' 0 3

A:

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A:

Q: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

A:

Q: Find the derivative for x+1 a)f(x)=- x-4 b)f(x)= sin' 2x Show the work on your notebook, take a…

A: (a) To find: The derivative of fx=x+1x2-4. Formula used: Quotient rule of derivative:…

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A:

Q: Calculate the derivative of the following functions. y = (cos x + 2 sin x)8

A: Given function is y=cosx+2sinx8.

Q: For the implicitly-defined function, calculate the derivative with respect to x. sin (7xt) = 5t (Use…

A: NOTE: Refresh your page if you can't see any equations. . take the derivative with respect to x

Q: Find the second-order derivative of the following function: f(x) = log2 cos x + ln π

A: We have to solve

Q: Find the derivative of the given function. 2 y = x sin x+x cos -3 dx

A:

Q: If f(x) = = f'(x) = 3x (sin x + cos x), find f'(x). Evaluate the derivative at x = 4. Enter an…

A:

Q: 3. y²(x + 2y) = 8

A: The Solution is dydx=-y2(x+3y)

Q: The 2nd derivative of the function x = Ci cosot + C2 sin ot with respect to t is

A: Given function is

Q: 2. Find the first derivative of the following expression: f(x) = (x2 + 1)sin a

A: take derivative  use the exponent rule

Q: d. x cosy + y sin x –1 = 0 3 х е. = 2 x y

A:

Q: f(x) = (x + 6 sin x) (1 – 5 cos x -

A: To find the derivative of:f(x)=x+6sinx1-5cosx

Q: c) Find the derivative of nh (cosu). Where n is 482

A:

Q: Find the first derivative with respect to the domain variable for the following functions. 12. i(x)…

A: The given function is:ix=e7xlnx2To find its derivative.

Q: 3. Find the derivative of the following function. 8(x) = cos"(vx)

A:

Q: Find the equation of the tangent line to the function f (x) = e*²-1 ln(x + 1) when x= 0.

A:

Q: Find the first derivative or f(x) of the following functions using the techniques of integration.

A:

Q: Find the derivative: 1+e5 f(x) = = COS 1.

A: The given function is f(x)=cos1+e5x1-e8x

Q: Find the actual error when the first derivative of f(x) = sin(2x) at x = n/8 is approximated by the…

A: