Given the functions f(x) = 2x* and g(x) = 3 · 3ª, which of the following statements is true?

Q: Given f(x)=−2x^2+4x+13, find f′(−4) using the definition of a derivative.

A: f'(a) = limh→0 f(a+h)-f(a)h.

Q: Find the second derivative of the function.

A:

Q: find a general formula for f (n)(x). f (x) = x−3/2

A: Given, f (x) = x−3/2 To evaluate, fn(x)

Q: If f(z) = 7(x – 1) + 8 , what is the value of f(1) ? %3D

A: Given : f(x) = 7(x-1) + 8 To find : f(1) = ?

Q: Find f"(x), given that f(x) = 8 csc x+x* -7e2x -Vx²

A:

Q: 2. If f(x) = e*+ °, what is f"(x) ? x'+ 5

A: Given that f(x)=ex2+5 find out f11x

Q: If f (x) = (e²)² , what is f'(x) ?

A:

Q: Find the derivative of f(x) = -4x ( 3' *(3"). %D 3+4

A:

Q: f (x) = 3 · 5" + e 4x²+7¤

A: We have to find derivative

Q: Find a formula for f-'(x) and (f -1)'(x) if f(x) = V х-2

A:

Q: Given that f(x) =x+4 and g(x)=x -x, find (f+g)(1), if it exists. -X,

A: Given two functions f(x) and g(x). Then (f+g)(x)=f(x)+g(x)

Q: Find the second derivative of the function. f(x)= (3x³+6)* %D

A:

Q: Find ƒ‴ (x) , the third derivative of ƒ, and ƒ (4) (x) , the fourth derivative of f, for function.…

A: Derivate the expression three times  using the property d(xn)dx=nxn-1to obtain the third derivative…

Q: Find the third derivative of the given function. f(x) = (3x + 4)³

A: The given function f(x)=3x+43

Q: The derivative of f(x) = In(5x³ – 12) Is

A:

Q: Find the third derivative of the function f(x)=2x5-7x4+4x2-8x+11.

A: on doing diffrentiation with respect to x we will get

Q: find a general formula for f (n)(x). f (x) = x2e x

A: The first derivative of a function when equated to 0 gives us the critical points of the function…

Q: For the function f(x) = (5x² − 2)4 determine the second derivative in factored form.

A:

Q: Given that f(x) = 4x+1 and h(x) = x°, find (h o f)(2).

A:

Q: What is f′(x) if f(x)=40x^5/e^x

A:

Q: Find the first derivative with respect to the domain variable for the following functions. 6. f (x)…

A:

Q: Find ƒ‴ (x) , the third derivative of ƒ, and ƒ (4) (x) , the fourth derivative of f, for function.…

A: We have given the function f(x) = 7x4 + 6x3 + 5x2 + 4x + 3 To find the third derivative of the…

Q: Solve f(x) = 0, where f(x) = (x + 4)²(1 - x).

A: We have been given the function  f(x)=(x+4)2(1-x)

Q: Find the second and third derivative of the function (a) f(x) = x6 – 3.x5 – 41x – 73 - |

A:

Q: iven the function y=2x³-4x²+5,

A: Given, the function               y=2x3-4x2+5

Q: Determine the error term of for the formula: f'(x)  ≈ (1/4h) [f(x+3h) - f(x-h)]

A: In order to find the error term of the given expression, first find the value of f(x+3h) and f(x-h).

Q: If f (x) = /In(x²) + x², what is the value of f'(1)? %3D

A:

Q: If f(x)=x - 4 and g(x)= Vx – 2; which of the following is equal to x)?

A:

Q: Given that f(x) = 2x – 3  and h(x) =x2 - 4 Find:- i) f(-4) =   hᴏf(x)

A:

Q: Find the third derivative of the function f(x)=2x^(5)-6x^(4)+7x^2-9x+20

A:

Q: If f(x)= x – 4 and g(x)= Vx – 2; | f which of the following is equal to (x)?

A: Rational function value

Q: The derivative of is f (x) = 3x* + 7x² + 5x + 2 %3D

A: Given, f(x) = 3x4 +7x2 +5x +2

Q: If f(x) = e2" , what is f"(x)?

A:

Q: 2 If f'(x) = 3x? and X f (1) = 0, find f (x

A: Given  f'(x) = 3x2 - 2x3 ... (1) f(1) = 0

Q: Find the derivative of the function. g(x) = 8/ (5x2-6x)4

A: To find the derivative of the function

Q: Given the function: 0 < x < f(x) = 5<x< n 2 п — х

A: Given that f(x)=x,    0&lt;x&lt;π/2π-x,  π/2 &lt;x&lt;πTo the plot the graph and find the fourier…

Q: 6. Given that f(x) = 3x? + 1, find +h)=[(x)

A: Given f(x)=3x2 + 1

Q: The derivative of 4.x5 is f(x) f(x) = Зх-2

A:

Q: Find the second derivative of the function.   f(x) = x2 + 7x − 4

A:

Q: = x, find (f o g-3). Given that f(x)=2x+3 and g(x) (fo gX-3)-

A: (fog)(-3)=f(g(-3))

Q: If f(x)=D(x+1)x, then what is f"(1)?

A: The given function is  f(x)=(x+1)x To find f''(1) .

Q: Find the second derivative of the function. h(x) = 6x−2 + 7x2

A: Given function is hx=6x-2+7x2   Differentiate the function with respect to x.…

Q: Determine the 3rd derivative of the given function f(x) = (3x² - 5x + 6)4.

A:

Q: Find the first and second derivatives of the given function. f(x) = 5x3 − 6x2 + 6

A: The given function is f(x) = 5x3 − 6x2 + 6. The derivative of xn is given by: ddxxn=nxn-1 and…

Q: Find $ such that D =F. x - hg - hp-

A:

Q: 1. Find the derivative of the following. f(x)=13x* -7x²+5x²+11x+75 a.

A: Formulas:ddx(a f(x))=a ddxf(x)ddx(xn)=an xn-1ddx(a)=0;  where a is a…

Q: Given the function f(x)= x³-4x²+5x, find the open intervals where f is concave down, i.e. where the…

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.