Find the derivative of the function using the definition of derivative. 1- G(t) = 4t 2+ 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: Find the derivative of the function.

A: We are given with the function g(x) and need to find the derivatives

Q: Find the derivative of the function g(x) = x3/e2x

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Q: 2 a) For the function f(x) = X-3 , find f'(1) by using the definition of derivative.

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Q: 1. Find the derivative of f(x)= x(a+1), given a is a constant.

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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: Find the derivative of the function. g(x) = e-X + 3e2x - 2e-x + 11 g'(x) =

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Q: Find the derivative of the function. (x) = e+2 + 3 f'(x) : II

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Q: Find the derivative of the function. y = x2 csc x

A: The derivative of any function y=f(x) for the variable x is defined as the rate of change,for which…

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: 3. Find the derivative of the following functions, then use the derivatives to find the equation of…

A: Given function is f(x)=2x+3 find the equation of tangent lines at x=-1 and 2

Q: Find the derivative of the function. y = cos(a4 + x4) y'(x) =

A: The given function is y = cos(a4 + x4)

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: *(x) = x² +x – 7 , find f'(a) at a = -2 by using the definition of derivative.

A: To find the f'(a) using definition of derivative

Q: Find the derivative of the function and then evaluate at the given point. y = 2x - 3x; (- 1,5) f'(x)…

A: f'(-1) = - 7  The detailed solution is as follows below:

Q: b) Find the derivative function of f(x) = √5x - 1 using first principles.

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Q: Find the derivative of the function. y = 3 tan-(x - V1+x²) II

A: Consider the given function

Q: Find the derivative of the function y = In(5e – 9xe "). y = ||

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Q: calculate the derivative. g(x) = e2

A: We know that the derivative of a constant is zero. This result is used to prove the given statement.

Q: Find the derivative of the following​ function, where a and b are nonzero constants. y=asinx + bcosx…

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Q: Find the derivative of f(h(x))?  What is the slope of the tan line at x=0.  f'(x)=(3x^2)+3 h(x)=2x+1

A: Given function

Q: 1. x² - 2xy + y² − 6x + 2 = 0

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Q: (A) Find derivative of y = In V4+ a2

A: Given that a function y (x) and we find derivative of this. We know that : d(lnx)/dx = 1/x . Here i…

Q: Find the derivative of g(x) = e VIn x. %3D

A: gx=exlnx

Q: Using the definition of derivative, find the derivative of the following functions: (a) y = xvx² -2…

A: (1) Y = X*(X2-2)0.5       dY/dX = (X2-2)0.5  + (1/2) *(1/(X2-2)0.5) *…

Q: Find the derivative of the function. f(x) = ln(x2 + 1)2

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

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Q: y = In (*+1) °(x+1), (x+2)3

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Q: 4 a. Use implicit differentiation to find the derivative dy/dx of the given function. b. Find the…

A: The objective is to find the derivative and slope at the point .

Q: Find the derivative of the function g(t) = et et+e-t

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

A: Given, The function  y = 12x   We have to find the derivative of the following function.

Q: Solve for the derivative of the given functions using the Chain Rule formula. Let f(x) = √(x2 + 3x +…

A: (a) fx=x2+3x+1 Inner function : u=x2+3x+1. Outer function : y=u.

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

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Q: Find the derivative of the function g(æ) = (5æ² – 4x)e" - g'(x) =

A: →duvdx = udvdx + vdudx→dexdx = ex

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

A: Given:  Function  h(x)=-2x2x+32

Q: Find the derivative of the function. y= -3(6x2 +8) -6 dy dx (Type an expression using x as the…

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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) f(x) = (3x² – 5x + 8)35 (b) f(x) = cos(27.x)

A: First I have written the chain rule and then using it find the derivative of given functions.Also…

Q: Find the derivative of the function. h(s) = -2 -2V9s + 1 2 h'(s) %3D

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Q: Find the derivative of the function. 2 1 3 h(x) x3 h'(x) =

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Q: Calculate the derivative. g(x) = e2

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

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

Q: Find the derivative of the function g(x) et 2 + 3x g'(x) =

A: Given: gx=ex2+3x

Q: at x= 1

A: 9). Given function is fx=2ex-x. To find derivative of the given function at x=1. Solution:…

Q: Find the derivative of the function. f(x) = e-4x

A: The given function is:fx=e-4x

Q: (a) Find the derivative of the function f(x) = ex-1

A: Note: As per company policy we are supposed to solve only one question. So, kindly repost other…