1. Prove, using the definition of derivative, that if f(x) and g(x) are differentiable, then (10)- "2) • g(z) –S(2) - d(z) g²(x) (x) \ f'(x) · g(x) – f(x) · g'(x)

Q: Find the derivative of f(x)) at x = 3 if f(3) = 2, g(3) = = 5, f'(3) = 7, and g'(3) = 4.

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Q: A function f satisfies the following conditions. f(-3) = 2, f' (-3) = 0, f(-1) = 5, f' (-1) = 0, f…

A: Given that the function f satisfies the following conditions f(-3) = 2, f'(-3) = 0, f(-1) = 5,…

Q: Let f (x) = x² – 3. a) Use the definition of derivative to find f' (x).I (Write your answer in the…

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Q: 2 a) For the function f(x) = X-3 , find f'(1) by using the definition of derivative.

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Q: Let z = a + ib and f(x) = exp (zæ), then find the 1st and 2nd derivative of f(x).

A: Given: f(x)=ezxwhere,z=a+ib

Q: g (x) = /2-3x, %3D

A: Given: gx=2-3x we know that ddxx=12x                                     ..1

Q: If g(x) is the input to f(x), then the derivative of f(x) is ')(x) Select one: O True O False

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Q: 4. Let f be the function given by f(x) = 4-x. g is a function with derivative given by g'(x) =…

A: Given f( x ) = 4 - x

Q: -2 (a) Show that f'(x) using the definition of the derivative. (2x + 7)² (b) Find the equation of…

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Q: 18. If f (x) = es*, find (f-1)'(1) using Theorem 7 (Derivative of the Inverse Theorem).

A: We have to find derivative

Q: (d) Use the following table to evaluate each derivative. I 0 1 2 f(x) 1 3 -2 g(x) f'(x) 1 2 4 -3 0.5…

A: Since you have posted multiple questions i can do first question as per our company guidelines,…

Q: Let g(x) = 6x³ + 7x7 +2r Determine the derivative of g. 70)- Determine the slope of g at = 1. g'(1)…

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Q: 2) a) Let f(x) = 2* + 3x7. Find f'(x) and f" (x). b) Find the derivative f'(x) in the following…

A: a.)   Given f(x) = 2x + 3x-1/2 f'(x) , f''(x) are to be calculated. Formulas used here  ** y = ax…

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: Let g(u)= √8u+- 4 Determine the derivative of g. dg

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Q: 2. Let f(x) = cos(x). We will take derivatives of this function over and over. (a) Evaluate the…

A: Using standard formula of derivatives.

Q: 4. Find the derivative of r°(x+ 1)² y = Vr – 3x2 |

A: First i i have written the quotient rule of derivative , just use them for given function and get…

Q: 1 Let f(x) 4+ x -1 (a) Using the definition of derivative, show that f'(x) (No points if the…

A: the definition of the derivative is given by . the given function is  substitute x+h for x

Q: 1. Use the definition of derivative to find f'(1) 2r2 b) f(x) = Vx

A: Derivative of the function using definition