A graph of yY = f(x) is shown. In the same coordinate system, sketch a graph of the derivative func y = f'(x) over the interval [ – 4, 4]. | 4 -4 -3 -2 -1 3 4 -1 3.

Q: Find the first and second derivatives of the function. f(x) = In(x + 4) f'(x) = f"(x) I3D

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Q: Find the derivative of the function.

A: Given function is By using the properties of logarithm, ln(a/b)=ln(a)-ln(b) and ln(a^b)=bln(a), we…

Q: Please provide me with the solution to this problem. Please show the work and try to dumb it down so…

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Q: Find the derivative of f(x) = In(x² + 1) %3D

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Q: Use the chain rule to find the derivative of the function z = x2y3 − x along the curve given by x =…

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Q: Find the derivative of the function at the given number. f(x) = 3 – 4x + x², at -1 %3D f'(-1) = %3D

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Q: find the derivative of y with respect to the appropriatevariable. y = tan-1√(x2 - 1) + csc-1 x, x…

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Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 x - x sech-1 x

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Q: find the derivative of f (x) at the designated value of x. f (x) = 1x at x = 1/16

A: Given: fx=1x To find the derivative  Differentiate the given function with respect to x we get,…

Q: find the function with the given derivative whosegraph passes through the point P. ƒ'(x) = 2x - 1,…

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Q: 1. Find the first derivative by using the definition for f(x) = 3x² – 2x – 5, hence - find f'(-2)

A: Derivative of a function is ratio of difference in output and difference in input.

Q: y = In- e 2x+1

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Q: eリ- + 2y eTy x° +

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Q: Find the derivative of f (x) = x at x = -4 algebraically. f' (-4) =

A: f(x)=x3 Find f'(-4)

Q: find the derivative of f (x) at the designated value of x. f (x) = x3 at x = 12

A: The derivative of a function can be calculated by differentiating both sides of the function with…

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: y = x*(1 – In x4)

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Q: Find the derivative of the function. f(x): f(x) = 2xarccos(x) – 2/1 – x² 2arccos(x) + 2 2arc cos (x)…

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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.

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

Q: Find all possible functions f with the given derivative. f'(x)= 1/x-1, x is greater than 1

A: Obtain the all possible functions as follows.

Q: Find sixth order derivative of the function f(x)=(x-5)^7.cos(5x) by using Leibnitz theorem.

A: n! = n × (n-1) × (n-2) × (n-3) × (n-4) × ............ × 1

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. Sketch the graph of a tangent line of the function f(x) = at x = -1. And then find 1- x the…

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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: find derivative of the U function 1-x f(x) = sec-1. 1+ x ーオ

A: Explanation of the answer is as follows

Q: f(x) = x In x

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Q: 3/x +1 f(x) = X+2 at x = -1

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Q: 3x g(x)=e* In(4x+1) (с)

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Q: find the derivative of f (x) at the designated value of x. f (x) = x5 at x = 3/2

A: Given function is: fx=x5 We have to find the derivative of f(x) at x=32. Then we get,…

Q: Find the weak derivative of f() = |x² – x + 1/5| on the 1) interval (0,1).

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Q: Suppose that the first derivative of y = ƒ(x) is y'= 6x(x + 1)(x - 2). At what points, if any, does…

A: The derivative of the function y=f(x) is y'=6xx+1x-2. We have to find at what points, if any, does…

Q: Find the derivatives of the functions in Exercis

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Q: Find the derivative of y with respect to x. 1, 1+x2 In 1- x3 y

A: If you have function f(x) in the numerator and the function g(x) in the denominator, then the…

Q: Two equivalent forms of the Chain Rule for calculating the derivative of y = ƒ(g(x)) are presented…

A: Two equivalent forms of the Chain Rule for calculating the derivative of y = ƒ(g(x)) are presented…

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

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Q: Find the derivative of the function. g(x) = 9 + In(x)

A: We have to find the derivative of : g(x)=ex29+ln(x)

Q: Calculate the first derivatives of ƒ(x) = x2/(x2 + 1) and g(x) = -1/(x2 + 1). What can you conclude…

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Q: k(x) = x In x %3D

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Q: Find the derivative of the function by the limit process. f(x)=x2+x-1

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Q: Find the relative extremum of g(x) = x - 3x +1 by using first derivative test.

A: Let g(x)= x3-3x2+1 To find the relative extremum , here we use first derivative test In this method…

Q: The function f(x) whose derivative is sin x and whose graph passes through the point(0, 2)​

A: we have to find the function f(x) whose derivative is sinx and whose graph passes through the point…

Q: Find the derivative of the function by the limit process. f(x) = x3 - 9x + 1 f'(x)

A: We know,f'(x) = limh→0 f(x+h) - f(x)h  by limit processHere,f(x) = x3 - 9x + 1So,f(x+h) = (x+h)3 -…

Q: -5

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Q: B) Use the definition of differentiation to find the derivative of the function f(x) = 4- Vx + 3. Is…

A: Consider the function: fx=4-x+3 The definition of derivatives is given by the formulas,

Q: Suppose that the first derivative of y = ƒ(x) is y′ = 6x(x + 1)(x - 2). At what points, if any, does…

A: Here the first derivative of the given function is y’= 6 x (x+1) (x-2). If a function has zero…