Consider the function for x +0 f(x) 1 for x = 0. (a) Would you expect f(x) dx to be defined? Explain your answer.

Q: -What is the derivative of (x + 1)2 ? a) x? + 2 b) x c) x d) 2x+2

A: We will use chain rule of derivative

Q: Use differentials to approximate the change in y = f(x) from x = 4 to x = 4.1 for the function, f(x)…

A: It is given that,

Q: 2 a) For the function f(x) = X-3 , find f'(1) by using the definition of derivative.

A:

Q: Find the first derivative or f'(x) of the function below using the techniques of integration f (x) =…

A:

Q: Compute the derivative: d 4 dx x2 5 x=1 The derivative is:

A: The solution of the problem is given in the next step.

Q: Differentiate the function. y=(4x-4)° (3-x)? dy dx

A: Given query is to find the derivative of the expression.

Q: In the function:  f(x)= (3x^2)ln(x) , x>0 What are the inflection points of the function?

A: To find inflection points of the function we need second derivative of the function.Use product rule…

Q: 2. Compute the second derivative, f"(x), of the function f(x) = e*. %3D

A:

Q: Find the derivative of the function. f(x) = 4 tan -1 (e 11x) f'(x) = D

A:

Q: Fi ind the derivative with respect to x of f(x) = ( (3x³ + 8)' + 4) 9 + 2.

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: What is the millionth derivative of f(x) = e x ?

A: ex

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: Find the indicated derivative. df If f(x) = x3, find dx 8 df dx |x = -11 || X 32 X = 10 X 1 2 11

A:

Q: Q2. Use the definition of the derivative to find ý of the function y = sin(x). %3D

A: Here given function is  y = sin(x)

Q: Find the second derivative. 1 h(x) = x2 %3D | h"(x) = %3D

A:

Q: estion 9 Find the derivative of f(z) = 3z13 - 4+1. IDo? la sin (a) f' (x) =}

A:

Q: *(x) = x² +x – 7 , find f'(a) at a = -2 by using the definition of derivative.

A: To find the f'(a) using definition of derivative

Q: Find a nonzero value for the constant k that makes the function tan(kx) f(x) = 3 3x + 2k2,…

A: Given: f(x)=tan(kx)x,   x<03x+2k2,   x≥0 A function f(x) is continuous at x=a, if limx→a-f(x) =…

Q: 4 Find the derivative of the function y= f(x)= Jx(x-8). %3D

A:

Q: Q2/ Find the derivative of the function f(x) = V3x +1 by definition %3D

A:

Q: What is the derivative of the function f(x)= In(3x2) ? а. f'(x)= 2 b. None of these. с. 1 f'(x)= %3D…

A: We have given that  The function is f(x) = ln(3x2)

Q: V². Find the derivative of f(x) = In x² +1 %3D x(2r - 1)2

A: Derivative: f(x)=lnx2+1x(2x3-1)2ln(mn)=ln m-ln nln(x2+1)=12ln(x2+1)

Q: Suppose f(x) = In(x³ + 5x + 7). df Find the derivative dx f' (x) =

A:

Q: Q. / Find the derivative of y = (In(x²))'n(x²).

A:

Q: Compute the derivative function f'(x) algebraically. f(x) = 8x – 5 %3D f'(x) =

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

Q: %3D Apply the Chain Rule to find the tangent line to f(x) = 4v2x- 6e2-*at x = 2

A: We want to find the tangent of the given function at x=2 We know that slope of the tangent at a…

Q: Evaluate the function: S de x(x-2) -dx (x–1)³

A:

Q: Find the derivative of the function. F(x) = In(4 – x®) %3D f'(x) %D

A:

Q: (a) Find the derivative. = In(x) – In(x - 8) dy dx (b) Find the derivative. y = In X - 8 dy dx %3D

A:

Q: Compute the derivative: d x4 – 4 dx \ x2 – 5 lz=D3 The derivative is:

A:

Q: Find the derivative with respect to x if f(x) = e 2x %3D The derivative with respect to x if f(x) =…

A:

Q: Find the first derivative or f'(x) of the function below using the techniques of integration f (x) =…

A:

Q: Find the absolute extrema of the function f(x) = (x2 + 18)273 on the interval[-4,3]. Find the second…

A:

Q: Find the linear approximation of f(x) = sin x, for x close to 0

A: The given function is: f(x)=sin x To find the linear approximation of it close to 0.

Q: Find the derivative of the function. 4 f(x) x In(x) f'(x) %D

A:

Q: 3. Find the second derivative of f (x) = e²/*° and fully simplify your answer.

A: fx=e2x3

Q: Find f(2x)dx if f(x)dx = 1. Enter the exact answer. f(2x)dx

A:

Q: Evaluate the implicit function by finding dy/dx of x³+3y=3xy

A:

Q: What is the process for finding dy/dx when y is an implicit function of x? Illustrate with an…

A:

Q: 4 Find the derivative of the function f(x) = %3D x +7 Provide your answer below: f'(x) =

A: Given query is to find the derivative of the function.

Q: The function f(x)=|x|·sin(x) is differentiable at x=0.

A:

Q: Solve by definition of derivative if f(x)=x+Vx AND also Find x? w.r.t x*

A: fx=x+x Now by the definition of derivative, we have…

Q: IV. Obtain the 2nd Derivative of the given function. 7. 4y – xy? 1

A:

Q: 2. Find the derivative of (a) f(x) = x* + 4x 2 + 4e" (b) f(x) = 2 tan (x) – 6"

A:

Q: Show that, for a function f(x) with anti-derivative F(x), d s)ds f(x). %3D dx a

A: Suppose f(x) has an anti-derivate F(x), v(x) and u(x) are differentiable, then Leibniz's rule of…

Q: Q1) Compute the derivative of the function f (t)= | sin² x²dx. -t

A:

Q: Find the derivative of the function f(x) = (4x? – a – 4)* at x = - 1. %3D f'(-1) = Pr

A:

Q: (x+6)dx (x+2)?

A: To evaluate: ∫x+6(x+2)2dx

Q: Find the derivative of the function f(x) below. f(x)=ln(5−e^(−4x)) f′(x)=

A: Explanation: Given that, f(x)=ln(5-e-4x) Differentiate both sides with respect to x.…

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: