1. • Let a be an unknown constant and 1 f(x) = VT + +a. Find the derivative of f(r) with respect to r. What is the domain of the derivative f'(x)?

Q: 2. Find the derivative of a function at a certain number using the formula. f(x) – f(xo) f'(x) = lim…

A:

Q: 3) Find the second derivative of y with reference to x. xcosy = y

A:

Q: 5. Find the derivative of: a. f(x) = cos(e³x-4)

A:

Q: a. Find the derivative of f(x) = x2 - 5x at x. That is, find f′(x). b. Find the slope of the tangent…

A: Given: fx=x2-5x To Find: a. f'x=?b. Slope of tangent line of the given function at x=-1 and x=3

Q: 9) Determine the third derivative with respect to x for y = In x 10) Given f(x) 2x + 1 and f(1) 4.…

A: Find the derivative

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: 4. Find the first derivative of the given function using the Rules of Differentiation: a. h(x) = X-…

A:

Q: 10 Find the derivative f'(0) of f(x) = at x + 4 x = 0 using the laws of differentiation.

A: Derivative of the function

Q: SW Solve for the first derivative of ,(x+5) x' +e x³ +e + Vx f (x) = V0.1 at x= 0.05 using FCD BCD…

A: f'(0.05)=336.6222-333.90350.008=2.71870.008=339.8375 App value of f'=339.8375 exact value of…

Q: 1 Find the derivative of g(x)= (x)sec(x) + a+ x* + cos - sin(x)

A:

Q: 13. Find the derivative of y = in terms of f, g, h, f', g' and h', where f, g, and h are functions…

A:

Q: find the derivative of y with respect to the appropriatevariable. y = √(s2 - 1) - sec-1 s

A:

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

A:

Q: Compute the high-accuracy central difference approximation for the first derivative of y = cos x at…

A: There are three types of approximations to the derivative of a function f(x) at a point a. They are…

Q: 4. Find the first derivative of the given function using the Rules of Differentiation: а. h(x) —…

A: We need to find derivative.

Q: 4. Find an equation of the tangent line to the graph of f(x) = ln(x ^2 + 4) at the point (2, ln(8))

A:

Q: 26 Find the 155th derivative of (1 + x°)" at x = 0.

A: see 2nd step.

Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

A: Given function is : fx=3x-4x3

Q: Зх + 7 Calculate the derivative of f(x) at x = 0. Give an exact answer in decimal form. 4х — 5 f'(0)…

A: *The given function f(x) is, f(x)=3x+74x-5 Apply quotient rule on the above function to get the…

Q: 6. Find the first order derivative with respect to z of the function u = In/x2 + y2 +z²

A:

Q: 3. The derivative of f(x) = In x at x = 3 when h = 0.002

A: 3) To find the true error and relative error of the function: f(x)=ln x, x=3 &amp; h=0.002

Q: a.) z= 5.

A: We will find the second derivative of the given function in the following step.

Q: 1 6. Find the derivative of f(x)= 1 at the point 8, Vx+1

A: Given

Q: i. Show with the aid of Argand Diagram, where Ln(z³ + 3) is analytic . ii. Determine the derivative…

A: The given complex function is fz=lnz3+3.

Q: (3e)® arctan (3x³) In(e2«) arccos(5x) 1. Find the derivative of f (x)

A:

Q: 9. Find the derivative of the function using chain rule. f(t) = 3t In t

A: To find the derivative of the function

Q: Can you help me step by step with this problem?

A: Given,

Q: 2 6. Consider f(x) x + 1 a. Find f'(x) using the formal definition of the derivative. b. Find the…

A: Solve the function

Q: 1. Solve the first derivative of f(x) = e-2x In x at x = 0.5 using forward finite-divided difference…

A: To find the first derivative of the function f(x) = e-2xlnx at x = 0.5 using forward finite-divided…

Q: 10. Find the particular antiderivative of the derivative f'(x) = 3x-1 – x-2 where f(1) = 5.

A:

Q: 3. Find the first derivative of the function f(x)= 2x3-4x+1 using forward Difference formula if, X1…

A: Solution:

Q: (a) By using the chain rule and the derivative (1, if x>0 4 (1xl) ={-1, if x<0 %3D find (lx-x) vxE…

A: Use the chain rule to differentiate the above given function and than use the given derivative of…

Q: (a) Find the first derivative of the function y= la) with respect to x by using the chain rule.

A:

Q: 29. Prove the following derivatives by using the definition of derivative. (a) (") = n. dx nxn-1

A: topic - derivative and limits

Q: 3. F(x) = " In(x) (4t + et) dt. Find the derivative of F(x).

A: Given, F(x)=∫1ln(x)(4t+et)dt To find : Derivative of F(x) By using the second fundamental theorem of…

Q: (x² +SJ° In 14-X つ. dr

A:

Q: (a) Show that the derivative solution of this function y = x** is x(x*+x-1) [1+x In x (In x + 1)] dx

A:

Q: 1) Find the derivative of the given function with respects to 0 y = 3lan In 3

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

Q: 3. Find the derivative of (a) f(x) = (x + 2 sin x) (1 – 6 cos x), and (b) g(x) = sin x/ 7x

A:

Q: 2. Determine the 8th derivative of y with respect to x of the function 1 f(x) = 1+x2 and find the…

A: Taylor series

Q: 1/3 Find the absolute extrema of the function f(x) = (x + 16) on the interval [-5,2]. Find the…

A: To find: Absolute extremum of the given function.

Q: (4)The instantaneous rate of change of f(r) = e- at a = 1 is . .. (5) The derivative of f(x) = sec2…

A: (4) We have So we get the instantaneous rate of change of the function at  as .

Q: 3. Find the derivative of y with respect to the appropriate variable. x y= 6sinh :

A: Solution: y=6sinhx3

Q: Consider the function f(x) = x³ Q 2: Calculate its first derivative at point x = 3 numerically with…

A: We have given , f(x) = x3

Q: 1. Find the derivative of g(x): Int dt 1+t Cos

A: This will solve by Leibnitz theorem

Q: can you help me step by step with this problem?

A: Let z= 6x^2+1 Substitute that. Then take d/dx on both sides.

Q: What is the derivative of f(x)=−3cos(x)+4sin(x) at the point x=π/3? Enter an exact answer.

A: Given,  f(x)=−3cos(x)+4sin(x)   We have to find the derivative of fx  at  x = π3

Q: 1. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: