Find the derivative of the function using the definition of derivative. f(x) = 2.5x2 - x + 3.6 f'(x) = State the domain of the function. (Enter your answer in interval notation.) State the domain of its derivative. (Enter your answer in interval notation.)

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: 1-x e) f(x) = 1+x

A:

Q: Find the derivative. g(x) = tanh-1(x?)

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Q: Find the derivative of the algebraic function.

A: To find the derivative of the algebraic function. f(x)=3x-1x

Q: derivative of the function f (x) = xsec-1 (2x + 1)

A:

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: Find the derivative of the function. F(x) = /1 – 2x

A: Given, Fx=1-2x

Q: Find the derivative of the function f (x)=x-2r.

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Q: Find the derivative of f(x) = 2e%.

A:

Q: Find the derivative of the function. h(x) = ex² - > x + 5 %3D

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Q: Find the derivative of the function using the definition of derivative. 1 g(x) 8 + Vx g'(x) =

A:

Q: Find the second derivative of the function.

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

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

A: To find derivative of function.

Q: Find the derivative of the function f(x) = 4x

A: The given function is f(x) = 4x Formula used ddx(ax)=axln(a)

Q: Find the derivative of the function g(x) et 5x - g'(x) =

A: We have to use quotient rule for derivative and use  d/dx(ex)=ex d/fx(ax+b)=a

Q: Find the derivative of the function. f(x) = 8x

A:

Q: Find the derivative of the function using the definition of derivative. f(x) = rx + q

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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 derivative of the function.

A: Given function is hx=x+5x2+32 We have to find derivative of given function. To find derivative of…

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

A:

Q: Find the derivative of the function f(x)=x-2/2+x square root

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Q: Find the derivative of the algebraic function.

A: Given function is fx=3x-1x. To find the derivative of the function. Solution: Power rule of…

Q: Can you help me step by step with this problem?

A: Let's assume u = 3 + xsecxPlease note that the second term is made up of two functions of x and they…

Q: Find the derivative of the function. 2 + g(x)

A: We know that  ddxxn = n·xn-1

Q: Find the derivative of the function: f(x)=ln x^2(x-3)^3÷(x+1)^4

A: To determine the derivative of given function.

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

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

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Q: Calculate the derivative of the function. Then find the value of the derivative as specified. g(x) =…

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Q: Find the derivative of the function f(x)= xsinx+x^2e^2-1.

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Q: Find the derivative of the function f(x)=2x−73x−2 at x=2

A: topic - derivative of a function

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

A:

Q: find the derivative of the function f(x)=6x

A: We have to find the derivative of given function.

Q: Find the derivative of the function. f(x) = 4 3√x + 2cos x

A: The given function is ; f(x)=4/3sqrt(x) +2Cosx.

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 derivative of the function. Then find the value of the derivative as specified. g(x) =…

A:

Q: o f(x) = 4~/x+3

A: by using definition of a derivative.

Q: Calculate the derivative of the function, then find the value of the derivative at the specified…

A:

Q: Find the derivative of the function. f(x) = In x+ 2 f'(x) =

A: We have to find the derivative of the given function.

Q: Find the derivative of the irrational function y=2√x−33√x.

A: Given: y=2x-33x

Q: f(x) = log,(x² – x + 3)

A: Given: f(x)=log4(x2−x+3)

Q: Find the derivative of the function using the definition of derivative. 1 f(x) V5 + x

A:

Q: 14. Find the derivative of the function using the definition of derivative. f (x) = V1 – x

A: Derivatives

Q: Find the derivative of the function   f(x)=ln(x3(2x+1)/x^2−3)

A:

Q: 2) Find the derivative of the function f(x) = 3x² by definition

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Q: Find the derivative of the function: f(x)=ln  (x-3)^2÷(2x-1)^3

A: Given function is,

Q: Find the derivative of the function. F(x)= 1-6x

A:

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

A: Given

Q: Find the derivative of the function f by using the rules of differentiation. f(x) = (1 + 3x2)2 +…

A: f(x)=(1+3x2)2+4x3 Apply the rule of differentiation  WE apply power rule and chain rule to take…

Q: 3. Find the derivative of g(x)=

A: We will use Lebnitz rule to find the derivative Of g(x).

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: