Use the fact that the derivative of the function ​f(x)=4/x is f"(x)=-4/x2 to find the equation of the tangent line to the graph of​ f(x) at the point x=−7.

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

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Q: By using the definition of the derivative, find the for: - dx 1- f(x) = Vx

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Q: use the definition of derivative to find the equation of the tangent line to the graph of f(x) = x2…

A: To find the equation of tangent line at the given point.

Q: Find the derivative of the function by using the rules of differentiation. 1 f(x) = f'(x) =

A: topic - derivative of a function

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

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Q: Consider the function f(x)  whose second derivative is f"(x) = 10x+4sin(x) . If f(0)=2  and f'(0)=3…

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Q: What is the derivative of the function f(x)=1/x+1 at x=1?

A: To find out the derivative of the function at x=1

Q: What is the second derivative of f(x)=6x^4 at the point x=−2?

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Q: Let f(x) = x^2 - 4x + 1. What is the equation of the tangent line to f(x) at x = 2? Use the limit…

A: Please see the below picture for detailed solution.

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A: Given function is : fx=6x2 To find out slope of tangent at x=2 , Differentiate fx with respect to x,…

Q: Determine the derivative of f(x) =2x/x2+1 using the quotient rule and find the equation of the…

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Q: Find the derivative with respect to the independent variable. f(x) = cos (- 23x) f'(x) =

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Q: Find the derivative of f(x) = Inx + 1].

A: f(x) = ln [x2x2+1]f'(x) = ddx[ ln [x2x2+1] ]f'(x)= 1 x2x2+1 ddx[x2x2+1]

Q: Find the derivative with respect to the independent variable. f(x) = tan (14x) f'(x) =O

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Q: Find the derivative of f(x)=[sin(3x)]^3

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Q: 2. f(x) = x2– 5x + 6 at x 2 --

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Q: What is the derivative of the function with respect to x of (x + 1)³ – æ° -

A: Given : Function x+13 - x3   To find : Derivative of the given function with respect to x?

Q: F(x) 1+ xe

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Q: Compute the second derivative with respect to x of 3x3 + 8 y = at x = 1.

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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 an equation of the tangent line to the graph of f at the given point.

A: The equation of the tangent line to the graph of f at a given point x0,y0 is y-y0=f'(x0,y0)x-x0…

Q: Use the fact that the derivative of the function g(x)=√x is g"(x)=1/2√x to find the equation of the…

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Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

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Q: Let f(x) = x8 - 8x6. When the tangent line is vertical, what is the derivative of f(x)?

A: Here we will understand the vertical tangent line and we will find derivative of given function,

Q: Suppose that the second derivative of the function y = ƒ(x) is y′′ = (x + 1)(x - 2). For what…

A: For inflection point we must have y" = 0

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 curve f(x) = 3x² - 6x + 1. Use the result to find the slope of the…

A: Follow the procedure given below.

Q: Use the derivative implicitly to find the slope of the tangent line at the point ,0), Suppose y is a…

A: Given- siny+cosx=12 To Find- The slope of the above expression at the given point π3,0.

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(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: Find the derivative. Ni at

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Q: Use the definition to find the derivative of the function f(x) = Vx +1 and obtain the equation of…

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Q: Find the derivative of the function. f(x) = 18 In(x) %3D

A: Derivative Question

Q: Find the derivative of the function f(x) v4-x by definition

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

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Q: The derivative of xª at x = e is equal to .Soloot ono

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Q: Use the definition of derivative to find the slope of the tangent line to the function f(x) = V2x at…

A: Let's find.

Q: Use a quick approximation to estimate the derivative of the given function at the indicated point.…

A: f (x) = 1 − 2x  point,  x = 2 To use quick approximation to estimate the derivative, f'(2).

Q: = Use the limit definition of the derivative to find the slope of the tangent line to the curve 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: The tangent line to f(x) = x² at x = –3.

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Q: Find derivatives of f(x) = {x+- 1 and find the line tangent to it when x = 1

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Q: Find the second derivative of the function f(x) = sec2x

A: Given: f(x)=sec2(x)

Q: .If f(2) = 3 and f'(2) = 5, find an equation of the tangent line at the point where x=2.

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Q: What is the derivative of the function B(x)=3/(x+2) at x=a?

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Q: Calculate the derivative of the function y=x2−x−1x without using the quotient rule.

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Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

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Q: Use the definition of derivative to find the tangent and normal equations of f (x) = (x – 3)2 %3D

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

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Q: 2 Use the definition of derivative to find the equation of line tangent to f(x) = 2 through x = 3.

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: