Use the table to the right to find the given derivative. f(x) f(xX) g(x) f(X)g(x) 3 2 5 4 4 3 1 2 (x),8 AR -OSimpity your answer)

Q: Jse the (first principles) definition of the derivative to find g'(x) if g(x) = I+ 2

A: Explanation of the answer is as follows

Q: Assume that f(x) is differentiable. Find an expression for the derivative of y at x =1, assuming…

A: Given, f(1)=4, f'(1)=-1 y=4xf(x) y'=(4xf(x))' =>y'=4(xf(x))'

Q: Using the definition of the derivative, find ƒ′(x) . Then find ƒ′(−2) , ƒ′(0) , and ƒ′(3)  when the…

A: Given function is: fx=-3x

Q: b) Find the derivative of f at the point P( – 3, – 2) in the direction of ü = ( – 1, – 1) fu( – 3, –…

A: The given function is fx,y=-0.02x2y3. Compute the gradient of f as follows. ∇fx,y=∂∂x, ∂∂y…

Q: Find the indicated derivative. x2 Find f(3)(x) if f'(x) = x2 + 6 f(3)(x) =

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Q: 1. Using the definition of derivative, find the derivative of the following functions: (a) y =xvx² –…

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Q: Assume that f(x) is differentiable. Find an expression for the derivative of y at x= 1, assuming…

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Q: Using the definition of the derivative, find ƒ′(x) . Then find ƒ′(−2) , ƒ′(0) , and ƒ′(3)  when the…

A: fx=32x Now,…

Q: 11. Given the function below, what is its derivative? * f(x) = 2x - √x f'(x) = 2x C f'(x) = 2 - a 1…

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Q: Find the derivative. f(x) = tanh(x) f'(x) = Need Help? Read It

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Q: Using the definition, find the derivative of f(z) = 3 z4-6 z? at point z= 0

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Q: Answer B True False The derivative of the function y=x²log (1-x²) is x² y=2xlog (1 - xảy - 2 1-x

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Q: Graph of derivative of function, f'(x), is given. y= f'(x) 1 5 7 8

A: We know that when f'(x) goes from negative to positive then f(x) will be decreasing and then…

Q: Using the definition, find the derivative of f(z) = 3 z4-6 z at point z= 0

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

Q: f(x) =e*(cosx) . Find the derivative of

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Q: Evaluate the derivative of the function at the given point. 1 y = ,t 3 4t + 7' y' =(Type an integer…

A: y=14t+7 take derivative y'=ddt14t+7 y'=ddt4t+7-1 y'=-14t+7-2ddt4t+7 y'=-14t+7-2·4 y'=-44t+7-2…

Q: Compute the derivative function f '(x)algebraically.  f(x) = x2 − 5

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Q: Let y" = e* (g(x)) be the second derivative of Y = Determine the value of g(x) if x =-3.8. (Us three…

A: g(x) is obtained by differentiating the y two times.

Q: x + Va x2 1. Find the derivative of the function f(x) = in two different ways. Once with the…

A: 1 Given function,                  f(x) = x+xx2Differentiate f(x) with respect to x, using quotient…

Q: f(x)= 4/x , x=3. Use definition of derivative as x approaches 0

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Q: Find the slope of the graph of the function at the given point. Use the derivative feature of…

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

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

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Q: Compute the derivative function  f ′(x)  algebraically. f(x) = x3 + 4x f ′(x) =

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Q: 5 Find the f" of f(x) x4 II

A: The given function is fx=5x4

Q: Find the derivative of the function and evaluate f' (x) at the given value of x. (Simplify your…

A: Solution is given below:

Q: Assume that f(x) is differentiable. Find an expression for the derivative of y at x= 5, assuming…

A: GIVEN      Y= fx+1fx+x

Q: Find the derivative of the function. f(x) = ex2 + 6 f '(x) =

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Q: Find the derivative of the function. (2) = earcsin{z³) f'(z) = Need Help? Read It

A: Given query is to find the derivative of the expression.

Q: Find the derivative of f(x)=2ex.   f′(x)=

A: We differentiate both sides with respect to x

Q: Find the derivative of the function. f(x) = ex2 + 5

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Q: Use double derivative method for the function y=x*– 12x³ + 48 x²– 64 x to find i) the extreme…

A: Extreme values are values where function has maximum or minimum value. Concave up can be checked if…

Q: Find the derivative of the function. f (x) :f(a) D 0 and f' (a) = - 3 Find F' (a) given that F(x) =…

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Q: Using the definition of a derivative, what is y'(z) given that y(z) = z* +z² – 5z +3? (Do not…

A: Here we are going to solve only one question and for the remaining question post the question again.…

Q: Use limits to compute the derivative. f'(0), where f(x) = x ° + 3x +2 %3D f'(0) = (Simplify your…

A: The limit definition of a derivative, is given by f'(x)=limh→0f(x+h)-f(x)h

Q: find the derivative using the appropriate rule or combination of rules.

A: Consider the given function

Q: f(x)=1-x. Use the definition of the derivative to find f", f" and f""

A: Derivative by using definition

Q: Assume that f(x) is differentiable. Find an expression for the derivative of y at x = 3, assuming…

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Q: Assume that f(x) is differentiable. Find an expression for the derivative of y at x = 3, assuming…

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Q: termine the derivative of the function g(x) In x+ 10 %3D r- 10

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Q: (1) Using the definition of derivative, find the derivative of the following functions: (a) y = xVx2…

A: In the question it is asked to find derivative of the following functions.

Q: Estimate the derivative of the function f(x) =8-8x at the point x = 9. Select the answer rounded…

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Q: x – 4 Determine the derivative of the function g(x) In x + 4 Answer g'(x)

A: Proceed as shown below

Q: Evaluate the derivative of the given function for the given value of x. Show all work.

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Q: g(x) = 6e3.5x; h(x) = 6(3.5x) Find the derivative for f(x) = g(x) · h(x)

A: To find the derivative of given functions f(x).

Q: Use double derivative method for the function y=x- 12x + 48 x²– 64 x to find i) the extreme values.…

A: If a function is f(x), then we need to find the critical value by using f'(x)=0. Extreme values: If…

Q: Use the definition of derivatives using this formula f(x + h) – f(x) lim h 3. Find the derivative of…

A: We have,   According to the definition of derivative,

Q: 2. Using the definition of derivative, prove the following: 1 (a) f'(x) =E if f(x) = V

A: The given function is  f(x) = x1/3 To find f'(x)

Q: p>Find the second derivative of f (x) = x*e".

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Q: Using the definition, find the derivative of f(z) = 3 zª-6 z² at point z= 0

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