2. Given f(x) = x³ – 2x² + x + 2, find x e (-1, 3) such that f'(x) = 5. 3. Compute the derivative of f(x) = (".

Q: If ƒ(x) = x^n, n>=1, show from the definition of the derivative that ƒ′(0) = 0.

A: Given,

Q: 1. Find derivative of given function defined as follows. y = (8x²-3x³) ³

A:

Q: What is the first derivative of s(x)=(7x)3x at x=4?

A: To evaluate s'(4)

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: When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .

A: Given Data The function is f(x,y)=3xy²-xᶟ.   Differentiate the function f(x,y)=3xy²-xᶟ with respect…

Q: Find the derivative of function.

A: The given function is f(x) = ln(xex+2).We have to find the derivative of this function with respect…

Q: What is the derivative of 1+x3 at the point (1, )? O 1/4 O- 1/4 O 1

A:

Q: Find the derivatives of the functions in Exercis y = (1 + 2x)e-2x

A:

Q: 4) Find the derivative of the function: x* cos x h(x) %3D Vx2 + 1

A: Answer

Q: ; Compute the derivative of the function: f (x) = (+ Inx)² а.

A:

Q: Calculate the derivative of the following function. 7 y = sin '(cos (3x)) If the Chain Rule only…

A: To find the derivative

Q: Find the derivative of f(x) = Inx + 1].

A: f(x) = ln [x2x2+1]f'(x) = ddx[ ln [x2x2+1] ]f'(x)= 1 x2x2+1 ddx[x2x2+1]

Q: y = Arctan√3x−4/4 2. y = 2 Arccos ( 1 -x/2) + √4x − x2 3. y = ln (x3(x−1)/(x−2)^2) 4. y…

A: d2dx2arctan3x-44=d2dx2arctan3x-42=ddx1x3x-4=-9x-82x23x-43x-4…

Q: y = (Arccos 3x³)³

A:

Q: Find the derivative of the function.

A: Given that, f(x)=ln(x-1)   As we know, ddxln(x)=1x Chain Rule Of derivative, If…

Q: 4. Find the first order derivative with respe. to x of the function u = In/x2 + y2 + z2 %3!

A: The function is u=lnx2+y2+z2

Q: Find the most general anti-derivative of f(x) = 9Vx +1+ cos x.

A:

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

A: The given equation,

Q: 15 - What is the approximate derivative of f(x) = 5x° + 4x? if we use forward difference method,…

A: Derivative of function at any point gives the slope of tangent to the function at that point.…

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

A:

Q: 1 14) Use the definition of derivative to find dx 3- х.

A:

Q: Determine the second derivative of f (x) = x²e* at x = -2 with a step-size of h=0.50 using Central…

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

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

A:

Q: 5. Find the derivative of y = In(cos v3x + 2 ), by using chain Rule.

A:

Q: 1) Find the second derivative of f(x)= 24\x . (6) 2) If y = cos x, what is y (x)?

A: To find the derivatives of the given functions.

Q: 2. use the fundemental derivative formula to differential the folwing at x=2 • gex) = 3x-1 2メ+1 (1o…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: What is the value of the first order derivative of the closed function given as…

A:

Q: 5. Find the first order derivative with respect to y of the function U = In/x² + y² + z²

A:

Q: Find the weak derivative of f() = |x² – x + 1/5| on the 1) interval (0,1).

A:

Q: 4. Compute the second derivative with respect to x of 3x³ + 8 y : at x = 1.

A:

Q: Approximate the derivative of f(x) = x² + 4x + 5 at x = 3 using the forward, backward, and central…

A: f(x) = x2 + 4x + 5 h = Δx = 2 xi = 3         f(xi) = 26 xi+1 = 5          f(xi+1) = 50 xi-1 = 1…

Q: What is the approximate derivative of f(x) = x2e* , using backward-difference approach at %3D x-2…

A: The main objective is to calculate the value of the derivative of the function f(x)=x2ex at the…

Q: (b) Use implicit differentiation by partial derivative to solve for dx of the function 5x + xy 4y.

A:

Q: Find the derivative of f(x) = e" – a3 +In(x) - In(x)

A:

Q: 2. Prove from the definition of derivative that for n EZ, d ng"-1 dr

A:

Q: 4. F(x) = (1-t) dt

A: To find the first derivative

Q: Y= In (In2 (1-x))re?

A:

Q: Calculate the derivative of the following function. y= sin (cos (3x)) If the Chain Rule only needs…

A: In the question we have to find derivative of the given function.

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: 16. What is the derivative of the function: * y = sin(6x² - 1) y = 12x cos(6x² - 1) y' = x cos(6x² -…

A: Solving the problem by finding the value of the derivative.

Q: find the derivative of y with respect to x, t, or θ, as appropriate.

A: On simplification, we get

Q: If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.

A: Now the derivative of a function f at a point 'a' is given by,

Q: Compute the derivative for y= (e^-4x sin^2(x)) / (x^2 + 3x + 1)

A:

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

A:

Q: 8. Find the derivative of y = In(3t) dt.

A: To Determine: Find the derivative of given integral:…

Q: Find the first derivative of x² + 3xy + y3 = 10 implicitly.

A: The given function x2+3xy+y3=10

Q: In x g(x) = 2

A: