2. Use the definition of the derivative of a function at a number to calculate f'(8) where f(x) is the function f (x) = v6x + 1.

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

A: Given,

Q: Find the derivative of the function.

A: Given function is By using the properties of logarithm, ln(a/b)=ln(a)-ln(b) and ln(a^b)=bln(a), we…

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 derivative of the function. f(x) = In(x + 1) f'(x) =

A: To find the derivative of the function fx=lnx+1

Q: Find the derivative of the function. f(x) = 4 3 VX + 2cos x

A: Here, the given function is: f(x)=4x3+2cos x

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

A: Answer

Q: What can we use to find the derivative of a function when it is impossible or difficult to isolate y…

A:

Q: A) Find an equation of the line tangent to the function of x + (y-x)' D9 atx 1. B) Using the…

A: Part A,Given,          The function is x2+y-x2=9 at x=1.

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: Find the derivative of y with respect to x. 2. y²(x + 2y) = e²

A: Given,

Q: 2 The derivative of (g(x))¯ is equal to (g '(x))¯. Select one: True False

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: Find the derivative of the function. f(x) = 2x In(x) f'(x) =

A: Let us consider the given function as: fx=2xlnx By using product Rule of derivative, we get:…

Q: find the derivative of f (x) at the designated value of x. f (x) = x3 at x = 12

A: The derivative of a function can be calculated by differentiating both sides of the function with…

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: Find the derivative of the function. 1 3x' g(x) = dt 1 + t4 Jtan x

A: Given : g(x) = ∫tanx3x211+t4dt

Q: Find the derivative of the function. x + 6 X-6 y' = y = In

A: I have appended the formula used in the solution part of the question.

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: If C(x)=x' + x°, evaluate the fourth derivative at x = 2. %3D

A: To find the fourth derivative of the function: C(x)=x5+x-3 at x=2

Q: 8. Find the derivative of the function. y= In(1+x)

A:

Q: Calculate the 4th derivative of the function y=x2/x−1 at x=2.

A:

Q: Obtain the derivative of the function y (3 sen(4x))° ( tgʻ(2x)) y = (sec(2x))* – 1

A: This question is based on Trignometric application and diffrentiation of function.

Q: Consider the function as folows:-   r(x) = 2x - 5 /(3x + 1)2 In general, how do you find the…

A: Given function: rx=2x-53x+12 We can write the function as rx=2x-53x+1-2 Differentiate the above…

Q: Find the derivative of the function. h(x) = x² arctan(5x) h'(x) =

A: h(x)=x2tan-1(x)

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

A:

Q: 3/x +1 f(x) = X+2 at x = -1

A:

Q: 3x g(x)=e* In(4x+1) (с)

A:

Q: Find the derivative of the function. • 2x2 g(x) = 1 dt 3 + t3 /tan x g'(x) =

A:

Q: find the derivative of f (x) at the designated value of x. f (x) = 1/x at x = 2/3

A: Given: f(x)=1x To find the derivative at x=23

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

A:

Q: 1, Find the first and the second derivative of f(x): f(x)=x

A:

Q: find the derivative of f (x) at the designated value of x. f (x) = x5 at x = 3/2

A: Given function is: fx=x5 We have to find the derivative of f(x) at x=32. Then we get,…

Q: Let f (x) = 7 cos(Tx). Find the twentieth derivative of f (x).

A:

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

A:

Q: 1. Evaluate the derivative of f (x)= sec(In(x²)). DO NOT SIMPLIFY.

A:

Q: Find the derivative of the function. 10 f(x) = + 6cos x Vx

A: Differentiate above equation with respect to x

Q: Use the definition to find the derivative of the function f(x) = Vx +1 and obtain the equation of…

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: Determine the 8th derivative of y with respect to x of the function : f(x) = 1 / 1 + x2 and find the…

A:

Q: 2. Find from first principle the derivative with respect to x of the function f(x)= Inx.

A:

Q: If f(x,y) is a real valued function of two variables then what is the second derivative of f?

A:

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: What is the derivative of the function B(x)=3/(x+2) at x=a?

A:

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

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

Q: 2. Determine the 8th derivative of y with respect to x of the function f(x) = 1 + x2 and find the…

A: fx=11+x2 Differentiate the above function with respect to x. f'x=ddx11+x2=2x1+x22 Again,…

Q: Suppose ln (x + 2y) = x4.Use implicit differentiation to find the derivative of y with respect to x.…

A: Differentiate the given function implicitly as follows.

Q: Find the derivative of f(x)= ln x^2/x^2+1

A:

Q: 2 Use the definition of derivative to find the equation of line tangent to f(x) = 2 through x = 3.

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.