Given f (x) =x+5 a) Find the inverse function (assume f is one-to-one), b) find the derivative of the inverse.

Q: Use the definition of the derivative equation (f(x+h)-f(x))/h) to find the derivative of (1/x).

A: The definition of derivative is given by,

Q: f (x) = (x² – 1)**1

A:

Q: Find the second derivative of the function. f(x) = 205√x

A: We use the power rule to find the first derivative

Q: find the second derivative of the function. \text { 101. } f(x)=\frac{x}{x-1}

A: Given: f(x)=x1-x

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A:

Q: Find the derivative of the inverse function for y=2x3−1 and calculate its value at x=2.

A:

Q: Use the definition of the derivative to find the derivative of the function f(x) = 3/x and g(x) =…

A: Given f(x) = 3x then f'(x) = limh→0f(x+h)-f(x)h= limh→03x+h-3xh= limh→03x-3x-3hx(x+h)h=…

Q: Find the derivative of the function 2- X= x"sin? (x³)

A: We know that, from the product rule of differentiation ddxfx·gx=fx·g'x+gx·f'x             ⋯⋯1 Now,…

Q: Given f(x) = x² + 1, x 2 0, Find the derivative of the inverse at the point (5, 2) (do not find f-1)

A: Let's find.

Q: Differentiate and find the second derivative. g(x)= ex(x3+2x) What is g''(x)=

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Q: Find the derivative of the function.. 8 7 h(x) 218 4 х - h'(x)=

A: To find the drivative of the given function y=h(x)

Q: Find the derivative of the function: f(x)=e^-2x - e^2x

A: To find derivative of function.

Q: Use the General Power Rule to find the derivative of the function. g(x) = v6- 7x

A:

Q: Find the derivative of the function. g(x) = 2(3 - 8x) g'(x)=

A:

Q: If f(x) = 3 + x + ex , find ( f-1)' (4)     The derivative of the inverse in 4

A: The given function is,                  f(x) = 3 + x + ex We want to find the value of (f-1)'(4). We…

Q: The derivative of f(x) = cos-(2x) is:

A:

Q: What is the derivative of f(x) =,csc 2x 2

A:

Q: By using the first principle, find the derivative of the following functions. 1.  f (x) = x^2 - x

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Q: Find the second derivative of function, and then find ƒ″ (1)  and ƒ″ (−3) .

A: Given, f(x)=9x3+1x On differentiating both sides w.r.t x we get:…

Q: Find the derivative of the function.

A: Given: fx=ln 3x To Find: The derivative of the given function

Q: How do you find the derivative of an inverse trig function?

A: Note that, there are six trigonometric functions which also have inverses. There are general formula…

Q: find the second derivative of the function. \text { 107. } g(x)=\frac{e^{x}}{x}

A: Here, the function is g(x)=exx. According to division rule of differentiation ddxuv=u'v-uv'v2,…

Q: Find the second derivative of the function. f(x) X - 9 f "(x) =

A:

Q: Find the derivative of the function

A: Given function:

Q: find the derivative of the function.

A: Here given as gx=3x-5 or   gx=3x-5x>535-3xx≤53

Q: Find the second derivative of f(x) = x+2 X- 2

A:

Q: find value of derivative f'(a) for the given value: f(x)=x2 + 3x + 1, a=3

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Q: Without finding the inverse, evaluate the derivative of the inverse at the given point.  f(x) =…

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Q: Find the derivative of (Hайдите производную) (Баллов: 2) f (x) = x(-24)

A: Given,          fx=x-2x

Q: What is the derivative of f(x)= -3

A: Given f(x) = - 3

Q: 1+x y = 3-x2 ||

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the derivative of f(x) = 3√x- 26

A: Please refer to the image below

Q: Find the second derivative of f(x)=x4.

A:

Q: Find the second derivative of h(x)=x2+3x-3 Simplify your answer, if possible.

A: Our objective is to find the second derivative of h(x)=x2+3x-3.

Q: Find the derivative of g(x) = ln(2x + 5)

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Q: Find the second derivative of the function. In(x) f(x) = + 6x? -4x° – 18xln(x) + 3-6 ln(x) + 12…

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Q: Use the appropriate Derivative Formula for the algebraic function below. x2+1 2. y = x2-1

A: y=x2+1x2-1In this we use quotient rule QUOTIENT RULEy=uvdydx=v.dudx-udvdxv2apply this rule in given…

Q: Evaluate the second derivative of the function below at (1, -2). y² = x³ = x + 1 -

A: To evaluate the second derivative of the function at the given point.

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

A: →duvdx = udvdx + vdudx→dexdx = ex

Q: Find the derivative of the function. f(x) = ∣x2 − 9I

A: We know that ddxu=uu×dudx

Q: Find the second derivative of the function. f(x) x x-2 f"(x):

A:

Q: Given the function y=x2−x. Find the derivative of the inverse function at x=1.

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Q: Use the definition of the derivative to find the derivative of the function g(x) = 4 –x², then find…

A:

Q: Find the fourth derivative of f(x)=3-1.

A: To find the fourth derivative of the function: f(x)=3x-1 Now that the nth derivative of the function…

Q: If the function of x, ƒ(x) = · then, the derivative of f(x) is:

A: We will find the derivative of f(x) as following

Q: Find the second derivative of f(x)=x^3 + x-5

A:

Q: Find the derivative of the inverse of the following function. Express the result with x as the…

A: Consider the given function, fx=12x-16 so, it can be written as, y=12x-16 now, replace x with y,…

Q: Find the derivative of the function. g(x) = ∣3x − 5∣

A: We have to find the derivative of the function, g(x) = ∣3x − 5∣

Q: Given f(x) = x-/2, x> 0, a) Find the inverse function (assume f is one-to-one), b) find the…

A:

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…

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: