show that flzi2)= f (2)f(2).

Q: use the Product Rule to calculate the derivative. f (x) = (3x − 5)(2x2 − 3)

A: use the Product Rule to calculate the derivative. f (x) = (3x − 5)(2x2 − 3)

Q: d the second derivative of the functi =) = [3x° +6}* a. f" = 90x*(6+3x)ʻ(24+90x°) b. f" = 90x*(6…

A: We have to choose the correct answer from the given options according to the given information

Q: Use the chain rule to find the derivative of f(x) = 3(9z* – 82®)5 - You do not need to expand out…

A:

Q: Let f(x)= (x^3+3x+2)^2 f'(5)= ?

A:

Q: Show that the derivative of FOx) =x² is f'x)=2x using the defimition

A:

Q: Differentiate f(x) =- from the first principles. x2+3

A:

Q: V7x+2-V6x+4 = )f(x مستمرة عند 2 = ۲ if x 2 and x # 2 1- قيمة الثابت الذي يجعل الداله (x-2) if x = 2

A: Continuous at x=2,  using rationalization

Q: Find the 2nd derivative of y = 3x6 + 7x %3D O 90x3 O 18x4+7 O 18x5 + 7

A: y=3x6+7xTo find the 2nd derivative

Q: Let f (x) = 5x, g(x) = 2x² + 1, & h (x) = 6x +2, find (foh) (x). Show your work using the Equation…

A: Given: fx=5x, gx=2x2+1 & hx=6x+2

Q: 25. If f(x) = 3x² – x + 2, find f(2), f(-2), f(a), f(-a),

A:

Q: Define Sx² – 5 if x 1 Calculate f(2).

A:

Q: ax+bx+4 ifgと- ニ bx*-2 × ifメ

A:

Q: Use the chain rule to find the derivative of f(x) = 4(8z³ – 32")² You do not need to expand out your…

A:

Q: Differentiate the function. y = In|4 – x – 4x²| (-1– &r) In| (4 – x – 4x?)|| y' = — х — 4х*

A:

Q: Find invers of function f(x)=1/2x+1

A:

Q: Which derivative rule(s) was (were) usec f(x) = 2 e* + 7lnx - Vx3 1 7 f'(x) = 2 ex + 3. 4 4

A:

Q: 6 Identify any point(s) of inflection of f(x) = -3x³ + 5x³ and justify. %3D

A: The given function is: f(x)=-3x5+5x3 To find the inflection point we have to check the concavity of…

Q: Find the critical points and apply the Second Derivative Test (or state that it fails): f (x) = x4 −…

A:

Q: When f(z) = 8z 4z +5, evaluate f(- 2) f(- 2) =

A: The given function is: f(x) = 8x2 - 4x + 5

Q: Find the point of f(x) = 2x3 - 9x2-17x - 3 is at [0, 00) on which concavity changes. %3D

A: We draw graph of given function.

Q: Describe the long run behavior of f(x) = 25 x + + 88x4 As x → 0, f(x) → ? - As x → 0, f(x) → ?

A: By using limit property, we find the behaviour of the given curve.

Q: What is the x=g(x) that will diverge the root of f(x) = x3 + 4x2 - 10?

A:

Q: Find the derivative of f(æ) = (– 72³ + 4x°) (5e* – 1) -

A:

Q: If f(x) = 5x' +x²+ 4, then f(-2)- --

A: Given : fx = 5x3+x2+4

Q: Find the extreme values of f (x) = 2x3 − 9x2 + 12x on [0, 3] and [0, 2].

A: To find the extreme values of fx=2x3-9x2+12x on 0,3 and 0,2. Solution: For finding the extreme value…

Q: in of (fo f)(x). (Enter your answer using

A: We have to find the following conditions according to the given information

Q: What is f(x)* h(x) if f(x)=6x²-2X+2 and h(x)=, 1?

A: f(x) = 6x2-2x+2  h(x) = 1/2x

Q: 1 If f(x, у, 2)- ôf then х— у—3z ду а. 1 (х- у-3-)2 b. -1 (х-у-3-)* С. 1 (х-у-3-)° d. 2 (х - у-3-)?

A: In Partial differentiation w.r.t y we treat x,z as constants.

Q: Find the derivative f(x) = √(7 + 4x2) - (1)/(5x2 + 9).

A: Consider the provided function, fx=7+4x2-15x2+9 Find the derivative of the function.…

Q: Suppose that f(x) = 17ex - exe Find f'(3)= ?

A:

Q: Let f(x) = 2x² + 8x – 9. According to the definition, -

A: Derivative: - Differentiation is the pace at which one quantity changes in relation to another. The…

Q: Find the derivative of f. f(x) = 3x4 + 8x3

A: f(x)=3x4+8x3differentiating both sides w.r.t. xf'(x)=34x3+83x2f'(x)=12x3+24x2

Q: 5. * y = ( In æ)²

A:

Q: Calculate R_5 for f(x)=2x^2+8x over [-1,1].

A: Given: fx=2x2+8x The interval is -1, 1

Q: If f(z) = 19z+ 24, find f'(-3).

A: Here, the given function is: f(x)=19x+24

Q: Find f'(2) for f(x) 2 (x-)-

A: Given; f(x)=(x-1/x)^2 We have to find f'(2)=?

Q: Differentiate from the first principle f(x) = x² +6x² + 3

A:

Q: The derivative of f(x) = (2x - 1)/(x2 + 1) is (-2x² + 2x + 2)/(x4 + 2x² + 1) Select the correct…

A: Derivative of the function

Q: What is f'(0)?

A:

Q: 1. Differentiate the function. f(t) = 3t6 2 5t + 4et – 10 --

A:

Q: What is the end behavior of f(x)?

A:

Q: Differentiate f(x) = x² – 3x by first principles“

A: Given f(x)=x2-3x

Q: Find the deivative of f(x) = Sec(4x72x)

A: Solution: The objective is to find the derivative of the given function

Q: Let f(x)=6sinx+4cosx f'(2pi/3)= ?

A:

Q: tion, 1 f(x) = wwww. (1+ 2x)3 I writing the firot fo

A: We are asked to find the maclaurin series.

Q: Find f. F"(x) = 20x³ + 12x²+ 4, f0) = 4, ( 1) = -1 Ax) =

A: Let us denote y = f(x). So,…

Q: let f(x)=√(2+2x)  f′(4)= ?

A: The function is

Q: If f(x)=4sin(x)+3x^x, find f'(3)

A: f(x)=4sin(x)+3xxnow differentiating both side with respect to xf'(x)=4cos(x)+3x.(xx-1)

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.