Find the derivative of the function using the definition of derivative. f(x) = ax + n f'(x) = State the domain of the function. (Enter your answer using interval notation.) State the domain of its derivative. (Enter your answer using 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: Find the derivative of the function.

A: Given: To find: Derivative

Q: Find the derivative of the function using Chain Rule. h(x) = (2x-6)-¹ (x²+3)

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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)

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Q: Find the derivative of the function. f(x) = ex In(x³) f'(x) = X

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Q: Find the derivative of the function. f(x) = In(x + 1) f'(x) =

A: To find the derivative of the function fx=lnx+1

Q: 2х- 3 3. У3 5x +1

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

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Q: What can we use to find the derivative of a function when it is impossible or difficult to isolate y…

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

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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) =

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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. X-1

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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. y In x2+9

A: Given function is: According to chain rule of derivatives:According to the quotient rule:

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

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Q: Find the derivative of g(x) =

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Q: Find the derivative of f (x) = 1x , x = 0.

A: Given: f(x)=x at x=0

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

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Q: 3) Find the derivative f(x) = xe-*In(x³) %3D

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Q: f(x) = x In x

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Q: Find the derivative of the following function by definition (from first principle): f(x)= x/(x-1)

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Q: Find the derivative of the function. 10 f(x) = 3 + 2cos x

A: Recall: dxndx=n xn-1 d(cos ax)dx= a(- sin ax) dc1f(x)±c2 g(x) dx= c1d[f(x)]dx± c2d[g(x)]dx

Q: Find the derivative.

A: Differentiate above equation with respect to x dydx=ddx{ln(x+1x3+1)}dydx=1(x+1x3+1)ddx(x+1x3+1)…

Q: 1. x² - 2xy + y² − 6x + 2 = 0

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

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

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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: Find the derivative of the function ° (2x + 1) f(x) = In x2 – 3 -

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Q: Find the derivative of the algebraic function.

A: Given algebraic function fx=3x-1x. Differentiating the given function with respect to x,…

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

A: by using definition of a derivative.

Q: Find the f derivative of x given f(x)=(3x)^-1

A: Calculation:Compute the derivative of f(x) = (3x)−1 as follows.

Q: Find the derivative of the function. x3 - 1 f(x) : x² +

A: dvu=udv-vduu2

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

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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 functionf(x) = (2 – x*)

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Q: Find the derivative of the function using the definition of derivative. 1 f(x) V5 + 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: Find the derivative of the function using implicit differentiation.  1.) x³-3x²y+2xy²=12 2.) x²-y²…

A: This question is related to implicit differentiation, We will solve it using given information.

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

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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

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

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Q: Find all possible functions with the given derivative. = రx = 1x 2x

A: The answer is given below

Q: Find the derivative of (x+5) / (x2-1) with respect to x.

A: Here we have to use formula of derivative  dxndx=nxn-1