Find the formula for the derivative of l(x) = 1 by using the power p2 rule. Confirm it using difference quotier Choose one l (x) 1 1 - (x+h)? lim h→0 Select the difference quotient for 1(x): h 1 (x+h)? lim h (x + h) – x lim h (x + h) – lim h→0 х h

Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 1 12. f(x) = 3…

A: Functions are given, we have to find the derivative at the given values.

Q: 2. Find the derivative of a function at a certain number using the formula. f(x) – f(xo) f'(x) = lim…

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Q: Find the derivative of a function at a certain number using the formula f(x) – f(x1) x-X1 x- x1…

A: Here's the solution, please have a look at it...

Q: Find the derivative of the following functions using the long method (limits) (a) x =t-5t- 3 (b) y =…

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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: 2) Use the limit definition to find the derivative of the given function. y = 3r2 – 2x

A: Limit definition of derivative is f'(x)=limh→0f(x+h)-f(x)h

Q: Find the derivative by the limit process. f(x) = 11 – x2

A: We have to find the derivative by the limit process where f(x) = 11 – x2.

Q: FIND THE DERIVATIVE BY THE LIMIT PROČESS OFF(x) = Vx+2.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: a. Find the derivative of f(x) = x2 - 5x at x. That is, find f′(x). b. Find the slope of the tangent…

A: Given: fx=x2-5x To Find: a. f'x=?b. Slope of tangent line of the given function at x=-1 and x=3

Q: -10 For f(x) = 2x-3 show that f'(x) = e using the limit definition of the derivative. ind the…

A: (a) f(x)=52x-3 f'(x)=limt→xf(t)-f(x)t-x        =limt→x52t-3-52x-3t-x…

Q: 2. Use the definition of derivative to find the derivative for f(x) = x2 + 3x . | f(x +h) – f(x) lim…

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Q: Find f'(x) using the delta definition of the derivative (i.e., limit process) vhere f(x)= x² – 5x…

A: Given that        f(x) = x2 - 5x + 12 Here we have to find f'(x) by using the delta definition of…

Q: Use the Quotient Rule to show that the Powers of x Rule applies to negative integer powers. That is,…

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Q: Use the graph of the first derivative function f'(x) to find x values at which function has relative…

A: First of all, consider the graph of f '(x).

Q: Use the limit definition of the derivative to prove the following special case of the Quotient Rule:

A: We have to prove the following derivative by using limit definition: ddxfxx=x f'x-fxx2 We know for…

Q: 4. Given f (x )=x'-12x +1. Use the second derivative test to determine the local extremum off (x).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. Let f(x) = x² ln x + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D

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Q: y = x*(1 – In x4)

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Q: Develop a general rule for the nth derivative of xf(x), where f is a differentiable function of x.

A: Given: the function xfx, where f is a differentiable function of x.

Q: Find the derivative of the function by the limit process. h(s) = −2 (square root of x)

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Q: Find the derivative of the function.

A: Given that, f(x)=ln(x-1)   As we know, ddxln(x)=1x Chain Rule Of derivative, If…

Q: 2. Find y' if y = 5x + 2 using the limit definition derivative.

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: fx て (X)

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Q: (d) VT tanr - 2 V lim /4 VT x(4x – 7) Hint: divide both parts of the fraction by VT x and represent…

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Q: Find the derivative of the function by the limit process.

A: The given function is fx=-5x. Obtain the derivative as follows.

Q: Consider the function as folows:-   r(x) = 2x - 5 /(3x + 1)2 In general, how do you find the…

A: Given function: rx=2x-53x+12 We can write the function as rx=2x-53x+1-2 Differentiate the above…

Q: for f(x) = 3-x/2x+3 , find the f'(-1) using the limit definition of derivative. then use it to find…

A: f(x) = 3-x2x+3using limit defination f'(-1) = limx→-1f(x) -f(-1)x+1…

Q: 2. Determine the true error and relative true error when approximating the derivative of f (x) = -x²…

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Q: find the derivative of y with respect to the appropriatevariable. = cosh-1 2√x + 1

A: Given: y=cosh-12x+1Here ,we havecoshy=2x+1Taking the derivatives on both…

Q: 11. Use the limit definition to find the derivative of f(x) = x² -2 x. 12. Find an equation of the…

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Q: Calculate the derivative of the function below using the quotient rule. x4 y = Vx + 2x4 f(x) = and…

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Q: find the derivative of the function f(x)=x^2 -2x using the definition of the derivative (a process…

A: Explanation of the answer is as follows

Q: Approximate the derivative of f(x) = x² + 4x + 5 at x = 3 using the forward, backward, and central…

A: f(x) = x2 + 4x + 5 h = Δx = 2 xi = 3         f(xi) = 26 xi+1 = 5          f(xi+1) = 50 xi-1 = 1…

Q: 2) Use the definition of the derivative, f'(x) = lim Ax-0 derivative of f(x) = 5x² + 3. f(x+Ax)-f(x)…

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Q: 1. Evaluate the derivative of f (x)= sec(In(x²)). DO NOT SIMPLIFY.

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Q: what the derivative fxy er hin ction Sas)=x'tan)

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Q: Find the derivative of the function f(x) = 4x2 – 13x – 30 by definition of derivatives f(x + h) –…

A: We have to find the derivative of the given function: fx=4x2-13x-30 by the definition of…

Q: Find the derivative of the following using the three-step rule 2. y=Va² +x

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Q: 1. Let f(x) =1. Using the limit definition of the derivative, find f'(x).

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Q: 2. Use the definition = f'(x) = limw-x- S(w)-r(x). to find the derivative of w-x y = tan x.

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Q: Let f(x) = /3x + 4. f(x) – f(a) Using the definition of derivative at a point, f'(a) = lim х — а…

A: The derivative of f at x = 1 is

Q: 2x 3, Use the limit definition of derivative to show that f(x) is differentiable at x2 – 3, r > 2 x…

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Q: Given f(x) = ||+x, at which point does the derivative not exist? Mathematically show that the…

A: According to question given that f(x)=|x|+x"A function f is said to be differentiable at a if  f'(a)…

Q: 2.Given f(x)=5Vx-1, find f'(x)using the limit definition of the derivative.

A: Given f(x)=5x-1

Q: find the derivative of f(x)=x/(x+2) using the limit definition of a derivative

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Q: f(x) = 3-x/2x+

A: First we have to find derivative of function at x =-1 by using given forumla-

Q: 5. Find derivative of the following composite function using the Chain Rule: f(x) = 3x2 + 8x, x(t) =…

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Q: 3 Find the derivative with gicapeet to X If f(0 = 0-7 The derivatie with reapeet to X If -7X is…

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Q: 7. Use the limit definition of the derivative to find f'(x). Then find the equation of the tangent…

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