Find the derivative of the function using the definition of derivative. 1 - 6t G(t) 4 + t G'(t) = State the domain of the function. (Enter your answer using interval notation.) State the domain of its derivative. (Enter your answer using interval notation.)

Q: 1. Using the definition of derivative, find the derivative of the following functions: (a) y= xVx-2…

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Q: f(x) = x2 - 3x + 5; x = 3/2, x = 2. Solve, a. Find the derivative of f at x. That is, find f′(x). b.…

A: Given function f(x)=x2-3x+5 and x=32,   x=2 To find: (a) f'(x) (b) the slope of the tangent line

Q: h(x)=In( x² ) +(x³-1 ) es*-10 Calculate the derivative at x=2, that is h'(2)=

A: Use chain rule of differentiation First differentiate with respect to x and then put x =2

Q: (a) Find the derivative of the function f(x) = S %3D ex-1 (b) Find the derivative of the function…

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Q: 3. Find the first and second derivatives of the function f (x) = e¬²

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Q: a. Find the derivative function f' for the function f. b. Determine an equation of the line tangent…

A: Given : f(x)=7x+1   To Find : a) Derivative of f(x) b) Tangent at point (a,f(a)) where a=5

Q: a. Find the derivative function f' for the function f. b. Determine an equation of the line tangent…

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Q: 4. Determine the derivative of the function with respect to x. 8sin?(x² + 2) y = 4tan²(x² + 2)

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Q: 1. Determine the first derivative of the functions below with the rules for deriving the function:…

A: A Given function is y=4x3+32. Use formula ddxxn=nxn−1 Differentiate  y=4x3+32 by using the chain…

Q: Зах + b Find the derivative of h(x) Assume a, b and c are | 5c constants. h'(x) = %3D

A: The objective is to find the derivative.

Q: Find the derivative of y with respect to x. + 1 5) y = sec-16x + -54 A) – 1 + (6x + 1)2 54 C) (6x +…

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Q: -2 (a) Show that f'(x) using the definition of the derivative. (2x + 7)² (b) Find the equation of…

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Q: a. Find the derivative function f' for the following function f. b. Find an equation of the line…

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Q: a) Find an equation of the tangent line to the curve. y=f(x)3x2-4x at x = 2. b) Find the derivative…

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Q: Calculate the implicit second derivative of b(z)=(x-5)^2 find the value of b''(-1

A: find the second derivative of the given function

Q: I am very confused on these two problems and I have homework due in 30 minutes.

A: Both problems concern finding deriviatives of functions ,using standard rules of differentiation

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

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

Q: Find the derivative of the function using the definition of derivative. G(t) =  1 − 5t 4 + t

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Q: a. Find the derivative function f' for the function f. b. Determine an equation of the line tangent…

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Q: f(x) = x2 - 4x + 7; x = 3/2, x = 2. Solve, a. Find the derivative of f at x. That is, find f′(x). b.…

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Q: a. Find the derivative function f for the function f. b. Determine an equation of the line tangent…

A: tangent of curve problem.....

Q: a. Find the derivative function f' for the function f. b. Find an equation of the line tangent to…

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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: 2. Fill in the appropriate derivative rule information for the function y (2-e")V6x-1 in the table…

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Q: t2 5. x= t-1 y = 12-1

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Q: Find the derivative of the function and then evaluate at the given point. y= 3x- 4x; (- 1,7) f'(x)=D…

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Q: 12 - 3t 2) Find the derivative of y= T+I

A: Given function is y=t2-3tt+1 Quotient rule of differentiation states that: ddxuv=vddxu-uddxvv2…

Q: Find the derivative of the given function at a given number 1. y=3x - 2 at f'(1) 2. y=x² -1 at f'(2)…

A: Find the derivatives at points. 1. y=3x2-2 for f'1. Apply derivative law: u±v' =u'±v'.…

Q: Find the derivative of the function. t(x) =  8x + 2x2/x   t'(x) =

A: Given function is t(x)=8x+2x2x

Q: a. Find the derivative function f' for the function f. b. Determine an equation of the line tangent…

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Q: Let g(x) = x* – 8x + 2. a) What is the derivative of g(x)? b) What is g'(3)? c) Find the exact…

A: Solve by derivation

Q: (a) Find the derivative at x = −1. (b) Find the second derivative at x = −1.   h(x) = 2x4 + 8x3 +…

A: (a) The given function is

Q: 1. Using the definition of derivative, find the derivative of the following functions: (a) y = xvx²…

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Q: 3. Find all possible functions with the given derivative y' =- 2

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Q: a. Find the derivative function f' for the function f. b. Determine an equation of the line tangent…

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Q: Obtain the derivative of the function f(2)% 3 -3a° – a* + 4x. Enter your answer as a function of a :

A: Given that f(x) = -3x2 - x4 + 4x  Find derivative of this function f(x). We know that derivative of…

Q: Find the derivative of the function. t(x) =  x2 − 8x3

A: Find out the function in t(x)

Q: (1) Using the definition of derivative, find the derivative of the following functions: (a) y = xVx2…

A: In the question it is asked to find derivative of the following functions.

Q: derivative of the function using the definition of derivative: g(t)=5/√ t

A: Given query is to find the derivative using definition of derivative.

Q: a. Find the derivative function f' for the function f. b. Determine an equation of the line tangent…

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Q: Using the definition of derivative, find the derivative of the following functions: 1 (c) y= 2x (a)…

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Q: a. Find the derivative function f for the function f. b. Determine an equation of the line tangent…

A: The objective is to find the derivative and equation of the line tangent to the graph of f at (a,…

Q: (x²+1)* Find the derivative with respect to x: y = In /1-x

A: The given function is: y=lnx2+151-x

Q: a. Find the derivative function f for the function f. b. Find an equation of the line tangent to the…

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Q: Find the derivative of the following function: y=1-x/√2-x

A: Given: y = 1-x2-x To find: Derivative of the given function.

Q: Use the alternative form of the derivative to find the derivative at x = c (If it exists). (If the…

A: Given hx=x+8, c=-8

Q: (x² + 4)(x – 2)² Vx +7 g(x) = In %3D Find the derivative of this function, g'(x).

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Q: Find the derivative of the function f(x) = 3x? – - 12x – 28 by definition of derivatives f(x + h) –…

A: A function is a relation which maps each value in its domain to exactly one value in its range. The…

Q: 2. f(x) = 2x – 5x%

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Q: e2x 2. Find the derivative of y = - (x² + 1)°(1 (1+ sin x)5

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