Find f such that f'(x) = 8x + 3x - 3 and f(0) = 4. %3D

Q: Find dy/dx by implicit differentiation   2x3 +x2y  -xy3  = 2

A:

Q: Find d2y/dx2 by implicit differentiation x3 + y3 = 1

A:

Q: finf dy/dx by implicit differentiation when x^2=(3x+6y)/(3x-6y).

A: The given function is: x2=3x+6y3x-6y

Q: max value for y

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 derivative of the function. y = 3x e -X - 3 ex3 dy dx

A:

Q: 0 and f'(x) > 2 for 1sxs4, how small can

A: It is given that f(1)=10, f'(x)≥2 for 1≤x≤4.

Q: п/4 sec z dz

A: By using integration formula, we calculate the given integral.

Q: FIND ANTI DERIVATIVE a) S 2. +9 dx x マ d x 1-4x6

A:

Q: Find the average rate of change of f(x)=x² – 5x from: x, =-1 to x, = 3

A: We will find the average rate of change of the function.  We know,  the average rate of change =…

Q: Find the instantaneous rate of change of y with respect to x at x=2 of the function y = 2x³ + 4 %3D

A: To Find: The instantaneous rate of change of the function y=2x3+4 at x=4. Given: The function is…

Q: Estimate ln(0.9) using a linear approximation

A: Given:ln(0.9)

Q: Find the indicated derivative. for y = dx 1 - 2x2 x* - 2x2 + 3 dy dx II

A: on doing differentiation we get

Q: 2x2+x dx x+1

A: Integration ∫2x2+xx+1dx

Q: Find the derivative of the function. y= log sv7x +3 dy dx I3D

A:

Q: 10. S(2x – 3) dx e 2x2 - ебх

A:

Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

Q: The total derivative of f(x,y) = ylnx  is

A:

Q: Find the relative extrema of f (x) = 7+ 144x – 9x? using both first %3D and second derivative tests.…

A:

Q: Find dy/dx by implicit differentiation   x2 + 5x + 9xy - y2=4

A:

Q: Find the derivative a) y = x sinh-(x) – Vx² + 1 b) y = cosh-(2Vx +1)

A: The derivative is calculated as:

Q: Approximate the length of the curve using n secant lines for n = 2; n = 4.y=ln x, 1>=x>=3

A: We have been given a curve y=lnx and we are supposed to approximate the length of this curve between…

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

A:

Q: Find the derivative. d [3x (x + 1)5] dx d dx [3x(x + 1) ³1-0

A:

Q: Integrate sec√x dx ÷ √x

A: We have to Integrate : ∫secxxdx Let x=t⇒12xdx=dt⇒dx=2xdt=2t dt Now, ∫secxxdx=∫sec tt(2t dt)=∫2 sec t…

Q: find dy/dx by implicit differentiation x3 + 4xy - 3y4/3 = 2x

A: Given: x3 + 4xy - 3y4/3 = 2x

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 dy/dx by implicit differentiation. x4 + yA 5

A:

Q: Estimate x² dx using left endpoints for n = 4 approximating rectangles. 3 x² dx is approximately

A: The equation of the integral function is ∫03x2dx. The left endpoints is n=4.

Q: Compute the derivative: x4 – 4 d - at x = 2 dx x2 – 5 - The derivative is:

A:

Q: 2. What is the average rate of change of the function f (x) = x² – 3x over the interval [1,1.01]?

A: use average rate of change formula .

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: What is the value of the function xcosnxdx if we integrate it using Kronecker' smethod?

A:

Q: Find the derivative 3x (x4+ 1)5 dx d 3x (x4 + 1)5]- dx

A: To find the derivative of [3x·(x4 + 1)5]

Q: Find F'(x). *sin(x) 8Vt dt F(x) = F'(x) =

A:

Q: Find the given derivative. DX 5x -- Dx 5x 1/3 1/3

A:

Q: The total derivative of f(x,y )=3 x+ 3 y-41n y is

A: Given function is fx,y=3x3+3y2-4 ln y find the total derivative  dz=fxx,ydx+fyx,ydy

Q: Differentiate the functions: 1. y = 3x – Vx 2. y = 2 – 3x – 3. Given the function f(x) = x³ – 5x +…

A:

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

A:

Q: The derivative of y=eSinh/x +cosh¬/x equals

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: What is the average rate of change of f(X)= X2-2 on the interval [-1,3]?

A:

Q: b) y = cosh(2Vx+1)

A:

Q: Find y'' by implicit differentiation. x2 + 4y2 = 4 y'' =

A: The detailed solution is as follows below:

Q: Approximate fls 3 + 2x* using Simpson's rule (n=6), then find the percentage of error after…

A: nhbgk

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. F(x,…

A: SOLUTION-

Q: Find the derivative of the function. 11) y = cos x4 A) dy -4 sin x 4 B) dY - sin x4 dx C) dy - -4x4…

A:

Q: Find the indicated derivative. 1- 2x2 x4 - 2x2 + 3 dy -for y = dx dy dx

A: Recall: uv'=vu'-uv'v2