Suppose that f(1) = -3, f(4) = -4, f'(1) = -3, f'(4) = -5, and f" is continuous. Find the value of %3D | xf" (x) dx.

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

A: To evaluate s'(4)

Q: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFf(x) = Vx+2.

A:

Q: Find dy/dx by implicit differentiation.

A: To find: The derivative of x3y-xy3=4. Concept used: Chain rule of derivative: fgx'=f'gx·fgx Product…

Q: Find the first derivative: y= ln v5x3 –- 2 5, O y = 222 %3D 523-2 O y' = 322 5z3-2 O y' = 622 5z3-2…

A:

Q: Compute dy/dx using the limit definition of the first derivative for f(x) = 3x2

A: Given function is f(x)=3x2. we have to find the derivative using limit definition .

Q: Find the derivative. 2 - - dy dx - if y(x) = 1 x + 3 dy dx ||

A: This question is based on Chain rule diffrentiation. d/dx{f(x).g(x)} = g(x)d/dx{f(x)} +…

Q: Find the derivative of the function y = (4x + 1)4(5x + 1)-5. dy (16x+4) 3 (4x+1)4 dx (5x+1)5…

A:

Q: Estimate the instantaneous rate of change of P(x)=5/x+2 at the point x=2

A:

Q: Estimate ln(0.9) using a linear approximation

A: Given:ln(0.9)

Q: Find the derivative of y= (2x³+x+1) 4(x²+3)5 (x4+3) 3 O A dy (4) (2x³+x+1) ³ (5) (x²+3) 4 dx 2(x²+3)…

A:

Q: 3. Solve the first derivative of f(x) = evx at x = 0.5 using centered finite-divided difference and…

A: To find the first derivative of f(x) at x=0.5 using centered finite-divided difference and a step…

Q: 10. S(2x – 3) dx e 2x2 - ебх

A:

Q: compute the derivative. f (x) = ln(ex − 4x)

A: We can use chain rule ( Nested function form ) of differentiation to find the derivative. According…

Q: If f(x, y) = ln(x + y), then total derivative or total differential of f at x = 3 and y = 20 is : Y

A: Given data: The given expression for the function is f(x,y)=ln(x+y). The given value of x is x=3.…

Q: Find the derivative of f (x) = Ln e*+1 using the limit process. %3D

A:

Q: sin x (cos x+1) dx 7. S (cosx +1)2

A: Given that: ∫sinx(cosx+1)(cosx+1)2dx           NOTE: As per our answering guidelines, we can only…

Q: Find the anti-derivative of: S(3x* – 6x)° (2x³ – 1)dx

A:

Q: 2. Find y' if y = 5x + 2 using the limit definition derivative.

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Find one anti derivative of (x+1)^2 and then find  integral(x+1)^2 dx.

A:

Q: Find the derivative of y with respect to x. y = tan 1 (In 4x) 1+ (In 4x)2 xV1+ (In 4x)² x(1 + (In…

A: We will find the derivative of y with respect to x as following.

Q: |х — 1 x5

A: Use the method of substitution to evaluate the integral. I=∫x−1x5dx=∫x−1x52dxLet u=xdu=12xdxSo,…

Q: Find the derivative of the function f(x) = 5ª+x² + log3 (In x). %3D

A: To find the derivative of the given function.

Q: Find dy/dx by implicit differentiation at point (0, 0) if x³y³-y=x

A: Here, x3y3-y=x

Q: Use implicit differentiation and solve for dy/dx if 6x+(x^3)y+3y^2=10.

A: The technique of implicit differentiation allows us to find the derivative of y with respect to x…

Q: Find the indic ed derivative. dz x2 for z = x2 dx 1 - x - 2x2 dz dx

A: Formulas:

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

A:

Q: Find the derivative of the function by the limit process. f(x) = 1/x2

A: Here the given function The first derivative of function f(x) is defined by limit prosses as

Q: dx V9-x2

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

Q: Find the function that passes through the point (1,2) and whose derivative is dy/dx = (2/x^3) - 4

A: Topic:- application of integration

Q: Find the anti-derivative of: f(3x^3+9x)^6 (x^2+1)dx

A:

Q: Let f(x, y) = cos(x+y²). Compute the rate of change in the direction of fastest increase for f at…

A: Find gradient and its magnitude then solve

Q: Find the derivatives of: d/dx (ex-e-x/ex-e-x) And the derivatives of: f(x)=ln((2x+1)3/(3x-1)4)

A: the given expressions is: dex-e-xex-e-xdx the given function is: f(x)=ln2x+133x-14

Q: Find dy/dx by implicit differentiation of 6x3+x2y-xy3=4

A: Product rule of differentiation:If f(x) is a function of u and v where both u and v are variables…

Q: 2. Use central difference approximations to estimate the first and second derivatives of y = e* at x…

A:

Q: Find the partial derivative. 4 = (x² + 6x – 3y)* - dz

A:

Q: Find the derivative of the function y, below. 9x(ln x + In 2) – 8x + v2 %3D

A: first, simplify the function  y=9xlnx+ln2-8x+2 y=9xlnx·2-8x+2 y=9xln2x-8x+2

Q: derivative of a Y with respect to x Y= ln (15x)+3x dy/dx=

A: Use formula of derivative to solve

Q: If fex, yJ-o find dy /af partial derivative off dx

A:

Q: Find dy/dx by implicit differentiation. 3+10xv+4x-5x=0

A: Given

Q: (d) Compute the driectional derivative of f at (1,2) in the direc- tion u = (e) • point (1, 2)? What…

A:

Q: consider a continuous function y=f(x) whose first derivative is y'=x(x- 2).

A: We can find the interval as below.

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

A:

Q: Find dy/dx by implicit differentiation at point (0,-2) if x^3-xy+y^2=4. O -2 -2/3 1/2 3/4

A: Implicit derivative at point

Q: Find the first derivative: In 2x f (x) 1- In 2x f(x) = In (sec x) f(x) = cos (In x) f(x) = In[cos…

A: we can answer only three subparts, or the first question and the rest can be reposted. No more than…

Q: 5, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4. ii, Find…

A: The objective of the question is evaluate area and find derivatives of given functions.

Q: Suppose x and y are functions of third variable t. In the equation *-+) , what are the values of the…

A:

Q: Suppose x6 e-5y = In (xy). Find Y by implicit differentiation. dx

A:

Q: What is the derivative of y = log, sec(e²x) Dxy = 2 e² tan (²) Dxy = 2 (log, e) e²x sec(e) tan(e) D,…

A: