f(z) – f(x) Use the formula f'(x) = lim to find the derivative of the following function. %3D Z-X f(x) = x+ 10 ..... f(x) =

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: Find the derivative of the function. y = tan an-¹ (√x-4)

A: We can find the derivative using chain rule as below.

Q: 2h lim h→0 h(/2x+2h+/2x)

A: Given, limh→0 2hh2x+2h+2x The definition of derivative is given by fx=limh→0 fx+h-fxh

Q: find the derivative of y with respect to the appropriatevariable. y = ln (x2 + 4) - x tan-1 ( x/2)

A: We use the chain rule and product rule

Q: 1) Find the derivative of y =-+x-1 %3D

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

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Q: Find the derivative of k(x) = log3(x) cos

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Q: Find the derivative. y= In x+3 %3D

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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: Find the derivatives of x^ x (x>0) with respect to x, find first principles

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Q: y = In- e 2x+1

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

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Q: 14. f(x) = 2 +3cos x

A: using basic properties and application of derivation we will solve this question.

Q: y = x*(1 – In x4)

A:

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 the derivative of the function. 1- e3x 1 + e3x y = cos y' =

A: Given that: y = cos1-e3x1+e3x To find: We have to find the derivative of the given function.

Q: f(x) = x In x

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Q: 1 14) Use the definition of derivative to find dx 3- х.

A:

Q: Determine the derivative of g ( x ) = 3 e-4 x*sin(7 x) with respect to x. = (x), 6

A: As per the guidelines, we need to author the 1st question.  We know that product rule is given by…

Q: Example 2: by using the definition of the derivative, find dy/dx of the function y = 5x + 8x - 3x +4

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Q: 1. x² - 2xy + y² − 6x + 2 = 0

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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: Example 2: by using the definition of the derivative, find dy/dx of the function y 5x' + 8x - 3x +4

A: We can use definition of limit In order to solve the given problem.

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. f(x) = ln(x2 + 3)

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Q: :) Given f(x) = |x|+x, at which point does the derivative not exist? Mathematically Question 4 (-…

A: We are given a function fx=x+x and we have to find the point at which fx is not derivable. We know…

Q: 3. Find the derivative of f(x). (a) f(x) = e cos x (b) f(x) = (2x³ 4x-¹) cotx -

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

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

A: Formula:

Q: Find the derivative of h(x) = (1+ cos x)*

A:

Q: Given f(x) = ||+x, at which point does the derivative not exist? Mathematically show that the…

A: According to question given that f(x)=|x|+x"A function f is said to be differentiable at a if  f'(a)…

Q: Find the derivative of g(x) = e-" cos(x²)

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Q: Find the derivative of y with respect to x    y=ln(x-7)

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Q: find the derivative of f(x)=x/(x+2) using the limit definition of a derivative

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Q: Find the derivative of the function by the limit process. f(x) = x3 − 2x + 1

A: Given function is fx=x3-2x+1. From the definition of derivative, we have f'x=limh→0fx+h-fxh Using…

Q: Find the derivative of f (x) =arcoth (e³" ).

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Q: c. Find the derivative of y =+- et x3 cOS X 2

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

A: The answer is given below

Q: If f(x) = sec (x) tan(x), then a particular anti-derivative of f(x), is -csc (x) + 1.

A: Firstly we have to find the antiderivative of function f(x)=secx tanx.then given the statement

Q: Find the derivative of the function. 10 f(x) = 3 + 4cos x %3D

A: Given that fx=10x3+4cosxTo find its derivative

Q: Find the derivative of the function. h(x) = ets. - x + 1

A: Differentiate w.r.t x

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

A: