For each of the given functions f(x), find the derivative (f-)'(c) at the given point c, first finding

Q: Use the definition of the derivative to find the slope of the tangent line to the graph of the…

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Q: Find the function whose derivative is 1-e2x

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Q: Find the derivative of the function f(x) = (In x)°.

A: Given that,             f(x) = lnx3 Differentiating with respect to x, we get                  f'(x)…

Q: If f(x)=4/x, find the derivative of f(x) at x=2 using the limit definition of the derivative at a…

A: given function f(x)=4/x we have to find a) the the derivative of f(x) at x=2 using the limit…

Q: Find the Derivative of f(x)= tan(- -3

A: We have to find the derivative of function: fx=tan x3x2-3 We know the formula of derivatives, d tan…

Q: Derive the formula for the derivative with respect to x of csc x.

A: We will write cscx= 1/sinx  Then we will use the quotient rule to differentiate

Q: 2х- 3 3. У3 5x +1

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Q: Find. the derivative of tan(x)). with respect to X 1- y3=

A: Explanation of the answer is as follows

Q: Find the derivative of each function at the specified value of x.

A: We have to find the derivative of the function at the given value of x: gx=ex sinπx, when x=0. We…

Q: Find the second derivative for the functions defined as follows ƒ(x) = (x2 - 1)2

A: Given function: fx=x2-12 fx=x4-2x2+1 Differentiate the equation w.r.t "x"…

Q: Q1. Find the derivative of f(x) = 2x -- by using the definition of derivative.

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Q: In the given question as follows, find the derivative of the function.   y = ln(2 - e5x)

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Q: Find the derivative of the function. X-1

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Q: Find the slope of the tangent line to the graph of the given function using the limit definition of…

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Q: 1 ソ= 1- x

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Q: Find the derivative using the Four-step rule f(x)=x/1-x

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Q: Identify the most appropriate differentiation rules to be used in finding the derivative of the…

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Q: Find the second derivative using implicit differentiation of the given xa + ya = aa

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Q: Find the derivative of the function using the definition of derivative. 1 f(x) x² - 36

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Q: Find the derivative of the function f(x) = {x3 - tan tan (4x2 -2)}4

A: The question is taken from the calculus in which we have to find the derivative of given function We…

Q: Find the derivative of the function. (x) - In(4 - x") f'(x) -

A: Find the derivative of the function.      fx=ln4-x8

Q: f(x) = Vet + evi

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Q: Use the definition of the derivative to find the derivative of, f(x)=6

A: topic - derivatives

Q: y=x²

A: I have stated the used formula in the solution

Q: Find the derivative of the function (slope of the tangent) using the definition at the point Xo=9…

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Q: Find the derivative of the function g(x)=x3∫x2tdt.

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Q: (x)

A: we have to find the derivative of the following functions using the different differentiation…

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

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Q: Find the derivative of the function and evaluate the derivative at the given x-value. f(x) = 5x +x…

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Q: Compute for the derivative of the function f(x)= Arctan (csc2 (3x2/3))

A: Some derivative formulas: ddxtan-1x=11+x2 ddxcscx=-cotx cscx Chain rule of derivative:…

Q: By using the definition of the derivative, find the equation of the tangent line to the graph of…

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Q: Find the derivative of x²e*.

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Q: Find derivative of the f(x) = sin-1*- 1 x+1 function

A: To find the derivative of the function

Q: Find the derivative of f(x) = et tan( – 82° + 5a“). - f'(x) =

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Q: Find the equation of the line tangent to the graph of the function f(x)=x-2x^2 at x=1 use the…

A: The equation of the curve is: f(x)=x-2x2

Q: Give three different notations for the derivative of ƒ with respectto x

A: Definition used -     Derivative of a function -       It is the rate at which the y value of…

Q: Find derivative of: g(x) = sin(x-3x2)

A: Given query is to find the derivative of g(x).

Q: Find the derivative of the following functions using the long method (limits)

A: Given: x= 12 t4-5t-3 To Find: limh→0xt+h-xth

Q: In(x-

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Q: Find the first derivative of the following functions

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Q: find the derivative of the given function. f(x)= 3x2- sin(x)/x

A: Given

Q: Find all possible functions with the given derivative. = రx = 1x 2x

A: The answer is given below

Q: Find the indicated derivative. f'(-5) = If f(x) = x², find f'(-5). X

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Q: function

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Q: Find the derivative of (x+5) / (x2-1) with respect to x.

A: Here we have to use formula of derivative  dxndx=nxn-1

Q: f(x) = 7xe

A: We can find the answer as below.

Q: flx)= -e, 1-x2 1-e

A: To find The derivative of f(x).

Q: The first derivative of the function f(x) is given by its graph.. f'(x) 3- 2-

A: A.  Function is increasing when f'(x) > 0  from graph  Function is increasing…