Use the definition f' (c) = lim,0 f(c+h)-f(c) to find the derivative. h f' (2) if ƒ (x) = 3 x+2 O -3/8 3/16 -3/16

Q: Find the derivative of the function. Simplify where possible. f(x)   = x In(arctan x)

A: Given: The above function contains two functions, so the product rule is used to differentiate.

Q: Find the derivative of the function by the limit process.

A: We have to find derivative of the function using limit process: fx=x+4 We know the formula of…

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 the function by the limit process. f(x) = 1/(x − 1)

A: We use the limit definition of the derivative

Q: Find the derivative of function.

A: The given function is f(x) = ln(xex+2).We have to find the derivative of this function with respect…

Q: Find the derivative of f(x) = x2 using the limit definition of derivative.

A: We have given function  f(x)= x2 So using definition of derivative  f'(x) = limh→0fx+h-fxh So,…

Q: Find the derivative of the function by the limit process.

A: Given: fx=x2+x-3 To Find: The derivative of the given function by the limit process

Q: Compute dy/dx using the limit definition of the first derivative for f(x) = 3x2

A: Given function is f(x)=3x2. we have to find the derivative using limit definition .

Q: FIND THE DERIVATIVE BY THE LIMIT PROČESS OFF(x) = Vx+2.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the derivative of the function by the limit process. f(x) = 6/x

A: Given fx=6xddxfx=limh→0fx+h-fxh

Q: Let f(x) = x^2 - 4x + 1. What is the equation of the tangent line to f(x) at x = 2? Use the limit…

A: Please see the below picture for detailed solution.

Q: Find the derivative of the function by the limit process.

A: Consider the given function fx=1x2   Derivative of any function fx using limit process is…

Q: Evaluate the derivative at x = 1 for y = In ()

A: For a function f its derivative is defined as f'(x)=limh→0f(x+h)-f(x)h. For some standard functions…

Q: Find the derivative of the function by the limit process. f(x) = √(x + 4)

A: Given function is

Q: Find the derivative of f(x) = Inx + 1].

A: f(x) = ln [x2x2+1]f'(x) = ddx[ ln [x2x2+1] ]f'(x)= 1 x2x2+1 ddx[x2x2+1]

Q: Find the derivative of f(x)=arctan(1/x) and simplify

A:

Q: By using the limit definition of a derivative, determine the derivative of f(x) = 1/x at x  = 2

A: By using the limit definition of a derivative, determine the derivative of f as shown below:…

Q: 2. f(x) = x2– 5x + 6 at x 2 --

A:

Q: Find the general anti-derivative of f(x) = + Vx on a continuous interval.

A:

Q: F(x) 1+ xe

A:

Q: Find the derivative by the limit process. f(x) = 14-x²

A:

Q: Compute the derivative using derivative rules. y= cos(1/x) / (1 +x 2)

A: Derivative: The rate of change of a function with respect to a variable. y=fxy'=limh→∞ f(x+h)-f(x)h

Q: find the equation of the tangent line to the graph of f(x) = x^3 + 3x^2 at the point (1, 4) without…

A:

Q: Find the derivative of the function by the limit process.

A: Given: fx=x3-12x

Q: 3x g(x)=e* In(4x+1) (с)

A:

Q: Find the derivative of the function by the limit process. f(x) = 7x − 3

A: GIven function: f(x) = 7x − 3 Formula used:

Q: Find y' if y = 5x + 2 using the limit definition of derivative.

A: Given that  y=5x+2

Q: Find the derivative of the function. f(x) = arctan(3x)

A: We  can make it easier for you.

Q: Find the derivative of the function by the limit process. f(x) = 3x- 1 - (x), J

A: fx=3x-1

Q: Find the derivative of the function by the limit process. f(x) = x3 − 12x

A:

Q: Find the derivative at the given x-value with the appropriate rule. y=4-18sqrt x at x=4

A:

Q: Find The derivaTive of f(X) = -x²+ 3X + 2 Using the de finiTion of the derivative

A:

Q: what the derivative fxy er hin ction Sas)=x'tan)

A:

Q: Give the derivative of f(x) arctan an(e³*) at the point where x = 0.

A:

Q: Use the limit definition of the derivative to compute the equation of the tangent line of f (x) =…

A: We have to compute the equation of the tangent line of f (x).

Q: Find the derivative of the function by the limit process. f(x) = x2 + x − 3

A:

Q: Find the derivative of the function by the limit process. f(x) = 7x – 6 %3D

A: The derivative is calculated using the limit process as follows. f'x=limh→0fx+h-fxh Now, fx+h=7x+h-6

Q: Find the derivative by the limit process. f(x) = 11-x²

A:

Q: Use the limit definition of derivative to find the slop of the tangent line of f(x)=5x^3+x at (1,6).

A: The derivative of the function is defined by,

Q: Find the derivative of the function by the limit process. f(x) = 7

A: The given function f(x)=7. The derivative of the limit  for the function f(x) is defined by So, to…

Q: find the derivative by using the definition of a deriviative.f(x)= 1/3x+2

A: according to definition of derivative we will evaluate the derivative of f(x)

Q: Find the derivative by the limit process. f(x) = 13 – x2

A: Given that: f(x)=13-x2

Q: Find the derivative by the limit process. f(x) = 15 – x²

A: Givenf(x)=15-x2Step -1From the definition of derivativef'(x)=lim∆x→0f(x+∆x)-f(x)∆x

Q: Let f(x) : 3x Using the limit definition of the derivative, find the equation x +1 of the line…

A: Given data: The given function is f(x)=3x/(x+1). The given point is (a, b)=(2, 2). The expression…

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 the equation of the tangent line of f(x)=2x^2-4x+1 at (2,1) using the limit definition of a…

A:

Q: Use the definition of derivative to compute f '(0). e-1/x if x * 0 if x - 0 f(x) f '(0) -

A: The definition of the derivative is given by: f'(x)=limh→0f(x+h)-f(x)h⇒f'(0)=limh→0f(h)-f(0)h  ...…

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve…

A:

Q: 2 Use the definition of derivative to find the equation of line tangent to f(x) = 2 through x = 3.

A: