1) Find First. three derivative of F(x) at x.2.2 f(x) : 16 40 S2 -2 Ans: f= 19.5 f" = 13.2 f"- 6.
Q: 9. State the Second Derivative Test for functions of two variables z = f(x, y)
A:
Q: 2. (a) Find the derivative of f(x) = 2x2 – 2x + 2 from first principle sin x (b) If y = x + find x4…
A:
Q: Find the derivative of the function. 1 - e3x = cos y = cos 1 + e3x y' =
A: Differentiate
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: 5. Second derivative of y = 1+t)< t2
A: Given: y = 1+t2t2 To find: Second derivative of the given function.
Q: (a) Find the average rate of change of f(x) from x = 1 to x = 2. 7 (b) Using the definition of the…
A:
Q: 5. Find the third derivative of the function : 3 (ans. : - 8y y=Vx
A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…
Q: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 1 using a value…
A: The two-point forward difference formula to calculate f'(x) is f'(x)=f(x+h)-f(x)h, where h is the…
Q: Compute backward difference approximations for the first derivative of the function, y =[ e'nxP, at…
A: We have to compute backward difference approximations for the first derivative of the function,…
Q: Find the derivative of the function: f(x) = ln X x+1* Is there a shortest way? Please explain.
A: We can find the answer in the following steps.
Q: The derivative of function y = tanh¬1 (sec(3x²))
A:
Q: Determine the percentage relative error (In 2 decimal places) when we compare the derivative of…
A:
Q: 4. Consider the function f(x) = 2 cos x x2 find its derivative
A: (4) Consider the given function. fx=2cosxx2 The quotient rule is defined as. fxgx'=f'g-g'fg2
Q: 2) Find nth derivative of the following function f(x) = ex
A: Given query is to find the nth derivative of the expression.
Q: 10) Find the second derivative of k(z) = 4 cscz.
A: Given: kz=4cosecz for finding second derivative of given function, we find first derivative then…
Q: 5) Find the second derivative of f (x) = %3D ex plify your answer as much as possible
A: fx=1-2xexTo find the second derivative
Q: 13. Find the second derivative y “ of y = 5z2 +sinrcosz
A:
Q: Compute central difference approximations for the first derivative of the function, y = e'cos(x?),…
A:
Q: find the derivative of y with respect to the givenindependent variable. y = 2(s2)
A:
Q: 1) Find the derivative of the function 2 + X y = arctan V 2 – x .Simplify where possible.
A: Answer and explanation is given below..
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: 1 at x= 4 by using the 2Vx Q2. Find the slope of the tangent line to the function f(x)= definition…
A:
Q: Find the derivative of the function tanh-e* A. -1/2 csch x B. 1/2 csch x C. -1/2 csch 2x D. -1/2…
A:
Q: find th first derivative: x=2cos2 t/2
A: we need to find the first derivative of
Q: Use three-point midpoint formula to evaluate the first derivative of y = cos(x) at x =; using a…
A: The three-point midpoint rule to calculate f'(x) is f'(x)≈f(x+h)-f(x-h)2h, where h is the step size.
Q: Solve for the derivative of t y =2 V3-z Previous
A: This is a basic differentiation problem
Q: Q:1 Find the second derivative of f(x) = 2x5 - 3VX7 at x = 1 rounded to five decimal places.
A: To find the second derivative of f(x)=2x⁵-3x7/3 at x=1
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 & h=0.002
Q: a.) z= 5.
A: We will find the second derivative of the given function in the following step.
Q: 4. Compute the second derivative with respect to x of 3x³ + 8 y : at x = 1.
A:
Q: Use the power rule to obtain the derivative of the first term. 10(x-1/3) = 10( dx Submit Skip (you…
A:
Q: Compute backward difference approximations for the first derivative of the function, y = cos(sin(x)+…
A:
Q: find the derivative of y with respect to the appropriatevariable. y = (θ2 + 2θ) tanh-1 (θ + 1)
A: The given function is y=θ2+2θ tanh-1θ+1. Obtain the derivative as follows.
Q: 7. Find the nth derivative of y = 1//x.
A: Since you have asked multiple question, we will solve the first question for you. If youwant any…
Q: Give the derivative of f(x) arctan an(e³*) at the point where x = 0.
A:
Q: Find the derivative of y = csc¯(In sin (x))
A: use simple integration formula.
Q: Use forward-difference formula to evaluate the first derivative of y = cos(x) at x = using a value…
A: Given we have given the function y=cos(x) we have to find the first derivative of y = cos(x) at x =…
Q: Q2: What is the value of second derivative of f(x)=3 sin((1-x)/t) *
A:
Q: Compute central difference approximations for the first derivative of the function, y =[ elnx)2 , at…
A:
Q: Q3: find the derivative of the following: 1. y = lnx + √1-x² sech-¹x 2. y= sinh-1(tanx)
A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…
Q: 2. Find from first principle the derivative with respect to x of the function f(x)= Inx.
A:
Q: 2 a) FIND BY IMPLICIT DIFFERENTIATION: x*y³ = -8 dy dx b) EVALUATE THE DERIVATIVE FROM PART a AT THE…
A: Given: x4y3=-8
Q: Compute forward difference approximations for the first derivative of the function, y = e*cos(x²),…
A:
Q: I FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM х 1. y= Arctan- 3-V9-x²
A: As per the company guidelines we can solve first question. I hope that the given solution will help…
Q: 12. y= tanh(t2 +1)
A:
Q: 2x Find the second order derivative of y = Tan 1-x
A:
Q: Use forward-difference formula to evaluate the first derivative of y = sin(x) at x = using a value…
A: Given function is y=sinx. We have to evaluate the first derivative of y=sinx at x=π2 using a value…
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: 8) Find the first derivative of f (x) = sin 2 (x3).
A:
Step by step
Solved in 2 steps
- Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If V is the volume of such a cube with side length x, calculate the derivative when x = 5 mm. V'(5) = mm3/mm What does V'(5) mean in this situation? V'(5) represents the rate at which the volume is increasing with respect to the side length as V reaches 15 mm3.V'(5) represents the volume as the side length reaches 5 mm. V'(5) represents the rate at which the volume is increasing as x reaches 15 mm.V'(5) represents the rate at which the side length is increasing with respect to the volume as x reaches 5 mm.V'(5) represents the rate at which the volume is increasing with respect to the side length as x reaches 5 mm.1. Determine the -values where relative extrema occur for y = (x ^ 2 + x - 12) ^ 2 . Use the second derivative test, if possible.(i) Find the first derivative of the function: y = 4x - 2x3 + 5 (ii) Differentiate the following function: y = 2 – x4 + 3/x
- Solve the following problem usingpartial derivatives.A certain paper-cutting machine produces varioussizes when increasing the length of a rectangularpaper by 6 cm each second while simultaneouslydecreasing its width by 5 cm each second. At acertain instant, the paper is a square with side oflength 30 cm. What is the rate of change of the areaof the paper at that instant?10. Find the derivative of y with respect to x. y=(x^(6)lnx)^(4)the derivative of E(q) is-(q*(q^2-1))^-1. what's its global maximum and global minimum. Thank you!
- The United States population (in millions) is predicted to be P(t) = 317e0.01t, where t is the number of years after 2013.† Find the instantaneous rate of change of the population in the year 2029. (Round your answer to two decimal places.) million people per year Find the derivative of the function. f(x) = x − e−x f '(x) =Daily crude oil production by Pemex, Mexico's national oil company, for 2008–2013 could be approximated by P(t) = 0.017t2 − 0.4t + 5.23 million barrels (8 ≤ t ≤ 13), where t is time in years since the start of 2000.† Find the derivative function dP/dt dP dt = At what rate was oil production changing at the start of 2010 (t = 10)? Daily oil production was decreasing at a rate of million barrels per year.find th first derivative: x=2cos2 t/2