4. A) Find the inverse of the function f(x) = 4x³ - 2 %3D B) What is the value of f'(30)? (Use 30 as the input into the inverse function in part 4A)

Q: Compute the derivative.    f'(3),   f(x) = log5 x

A: Given: fx=log5 x  ……1   To find: f'3

Q: By using the definition of hyperbolic functions as exponential functions, show that sinh 3x = 3 sinh…

A: handwriting solution

Q: Find the derivative of the inverse function for y=2x3−1 and calculate its value at x=2.

A:

Q: Find the second derivative of the function. 10. f(x) = 4x3/2 11. g(x) = x-1 12. h(x) = sec x

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Q: Find the derivative of the inverse function to f(x)=ex-e-x

A:

Q: 1. Find the derivative of f(x) if f(x) = x7 + 10x5 – x² – 4

A:

Q: 1 Find the derivative of f(x) = 2x + 3

A:

Q: Find the second derivative of f(x) = (5+7x)e5". f" (x)

A: Topic :- Differentiation

Q: x4 -5 7) f(x) = In %3D

A: fx=lnx4-5x first, simplify the function  f(x)=lnx4x-5x f(x)=lnx3-5x now take derivative

Q: find the second derivative of the function. \text { 106. } f(x)=\sec x

A:

Q: Solve for the second derivative of the following implicit function

A: We can solve this as follows:

Q: Find the derivative of f(x) = 33x-1 O 33x-2 In3 O 33x-1 In3 33x In3 32x In3

A: (1). Given: fx=33x-1   As we know that; The Power law; ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: Give the derivative formula for the function g(x) 2.1X 2 g '(x)

A: The given function is

Q: x=1), 3. Y = In (x-1), (х-2)2

A:

Q: Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=2 and f'(0)=3, what…

A:

Q: How do you find the derivative of an inverse trig function?

A: Note that, there are six trigonometric functions which also have inverses. There are general formula…

Q: Find the derivative of f( x ) = æ° log3 (x + 4.5). %3D f'(x) =

A:

Q: Find the 3rd derivative, f(3)(x), for f(x) = 6x3/2+e-3x-sinx and simplify with positive exponents.

A:

Q: Find the derivative of the function

A: Given function:

Q: What is the inflection point of the function f(x) = x5 ln(x)?

A:

Q: Consider the function f(x) whose second derivative is f''(x)=4x+3sin(x)   If f(0)=3  and f'(0)=2…

A: detailed solution with explanation is given below

Q: Find the derivative of the function. f(x) = 2x2 In 2x f (x)= 2x[1+2 log(2x)]

A: fx=2x2ln2x

Q: Find the second derivative of function, and then find ƒ″ (1)  and ƒ″ (−3) .

A: given,        fx=1-2x4x+5

Q: What is the fourth derivative? x^12+1

A:

Q: Find the second derivative of the function. In(x) f(x) 6x2 f"(x) =

A:

Q: Find the second derivative of the function. f(x) = 5(2 − 7x)4   Show your work

A: y''=?

Q: Determine the first derivative of the ff. function y = 400(2)*+3 sin 3x

A: Given: y=4002x+3 sin 3x To Find: First derivative of the given function

Q: 3 Determine the 3rd derivative of the function f(x) = 2√√x-x³

A:

Q: 1 Find the derivative of f(x) 2x + 3

A: Since we have to find the derivative of f(x)=12x+33, so ddx(f(x))=ddx1(3+2x)3 -(i)By using the chain…

Q: Find the second derivative of the function. In(x) f(x) = + 6x? -4x° – 18xln(x) + 3-6 ln(x) + 12…

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Q: 3. Find the derivative of h()= 5²°-2z-1 %3D

A: We have to find derivative

Q: Find the first derivative formula for the function g, by using the definition found in section 2.2.…

A:

Q: Find the second derivative of the function. . f(x) = 4x3/2 : 1. g(x) = %3D X-1 .. h(x) = secx

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Q: 8) Find the derivative of each function: 2. a)g(x) = 3x +5x

A:

Q: Find the second derivative of f(x)=x(x^2+1)^3

A: Find the derivative of function:

Q: 33. Solve for the second-order derivative of the function below. Y = x 3x3 За

A: Differentiate two times wrt x

Q: Find the second derivative of the function f(x) = 8/(x − 2)2

A: Find the second derivative of the function f(x) = 8/(x − 2)2

Q: Explain in words and express mathematically the inverse relationshipbetween differentiation and…

A: We need to Explain and express mathematical relationship between the differentiation and integration…

Q: What is the inverse process of determining a function whose derivative is known?

A: The inverse process of determining a function whose derivative is known is called

Q: Discuss how the processes of integration and differentiation can be considered as “inverses” of each…

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Q: 8. Find the derivative of each function: (a) f (x) = (7* + 5x³)5 3 x+3 (b) g(x) = (*) 9х—1,

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Q: #12) Find the derivative of the function f(x) = 35x2-1

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

Q: Evaluate the second derivative of the function at the given point f(x)=9/√x+9    (0,3)

A:

Q: What is the derivative of f( x = zi; = x 3 ? Or(-) = 3 F(=) f'( x Of(2) = 3= F(=) OF(2) = }ei OF(-)…

A: To find the derivative of f(x)=x2/3

Q: 8. Find the derivative of the function f(x) = x ² - 10x + 3 using First Principles.

A:

Q: What is the graphical interpretation of the derivative of a function f(x) at a point x=a? If f(x) is…

A: 1st question: The graphical interpretation of the derivative of a function f(x) at a point at x= a…

Q: What is the derivative of f(x) : %3D (* - (= – 17)' 1)*)*

A: The given function f(x) = x2-(x-1)32. We have to find derivative of f(x). To find derivative we use…

Q: 6) Find the derivative of each function. a) f(x) = In(4x +7) %3D

A:

Q: Consider the function f(x) whose second derivative is f''(x)=8x+8sin(x). If f(0)=4 and f'(0)=4, what…

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.