Let f(x) = /7x – 6. Determine f -'(x). f (2) = [

Q: Compute the derivative of F(x) if F(x) = 9t dt F'(x) =

A: To find the derivative of integral, one have to use the fundamental law of calculus and substitute…

Q: Find the derivative of the function f(z) = (3x +1)In(4x+3) %3D and then evaluate it at x = 0. f' (0)…

A: Given : f(x)=(3x+1)ln(4x+3)

Q: 4) Calculate the first derivative of the following functions: 1. f(x) = In 2x2+1° 2. f(x) =…

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Q: Find the derivative of the function. f(x) = In(x + V7 + x²) f '(x) =

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Q: Use the first derivatives test to find local exterma of f( x) =x3 -12x on R

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Q: Compute the derivative of the given function. g(t) = 2t - In(2 – 5t) %3D

A: Given that: g(t)=23t.ln(2-5t)

Q: Find the derivative of the following function F(x) = :7 (21 – 1)° dt x4 using the Fundamental…

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Q: Find the second derivative [ f"(x)] of the given function: f(x) = eln Vx²+2 %3D (x2 + 2)) x(x² + 2)-…

A: Given problem:- Find the second derivative [f''(x)] of the given function:   f(x) = eln√(x^2+2)

Q: Find the derivative of the function #1) F(x) = In(2x+3)· (4x +7) tan(x) t +4 dt t2 +2 # 2) h(x)= |

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Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: write the function as a composite f (g(x)) and compute the derivative using the Chain Rule. y = (x +…

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

Q: Find the derivative of the function 3 f(x) = V (x² – 2)' at x = -1. f'(- 1) =

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Q: Find f'(a) using the definition of the derivative at a point for: f(x). 1 = √x at a = 4.

A: Find derivative using  definition of f(x)=1x at a=4

Q: Find the linearizationsof the following functions at x = 0. ex

A: fx=ex at x=0. Now differentiating with respect to x, we get f/x=dexdx=ex Now, f0=e0=1 & f/0=e0=1

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

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Q: Let f(x) = (x² + 3x)e*. Determine the value of the third derivative of f(x) for x = 0.

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Q: a) Calculate the derivative of f Cx) by first expanding and Simplifyıng the function fCx)=(2-3x) 2

A: Given,           fx=2-3x2

Q: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

Q: write the function as a composite f (g(x)) and compute the derivative using the Chain Rule. y =…

A: Given : The function is y = cos ( x3 ) .

Q: Obtain the first and second derivative of the following real-valued functions 1. ƒ : R → R, such…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Let f(x) = Cx + 7x if x< 4 x³ - cx if x2 4. For what value of the constant c is the function f…

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Q: Use the e - S definition to show that the function x- 1 f(x) = x +2 %3D is continuous at x = 3.

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Q: Let y be a function of x and suppose y=In(x²+y²). What is the correct result for the derivative of y…

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Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 4x/3 on the interval [0,…

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Q: Find the linearization of the function f(x)=ln(2x+3) at x=-1

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Q: Find a positive value, c, for x, thot satisfies the Mean valve Theorem for derivatives for…

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Q: b) Use the definition of the derivative to compute f'(x) for 1)f(x) = 2v-5x + 9, 2)f(x) = x sin 3x…

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Q: The derivative of the function y = x² In(x + 1) is:

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Q: Find the interval in which function f(x)=sin (log,x)+cos(log,x) is decreasing

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Q: F(x)=In(52x+n • (x+2) ) %3D

A: Find the derivative of the function

Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

Q: Find the derivative of the following function x7 F(x) = (2t – 1)³ dt х3

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Q: Use the first derivatives test to find the local exterma of f(x) =x3-12x on R

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Q: Use the second derivative test to find the local exterma of the function f(x) =x3+12x2-5 on R

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Q: Find the function with the derivative f'(x) 3x = e whose graph passes through the point P| 0,

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Q: Compute the derivative of f(1) = In(x In(x² In(r³))).

A: The given function f(x)=lnx lnx2 lnx3

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

A: Derivative of the function using definition

Q: Linearize f(x) = 5 cos x about x = pi over 2. f(x) = -5x

A: linearization around x=a is given by :L(x)=f(a)+f'(a)(x-a)

Q: Evaluate the 3rd derivative of M with respect to (x) M= x6 y3 Cos (x6 y3) if x =6 and y= 3

A: The function is M=x6y3cosx6y3. Using implicit differentiation, find dydx.…

Q: Find the derivative of g(x) = J2x u²+1

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Q: Find the derivative of f(x)=

A: We use the quotient rule of logarithm to simplify the expression

Q: The general anti-derivative of the function f (x) - In(x) is given by x In( x)+ C Inx)-x+ C x In(x)…

A: The integral (anti derivative) of fx=lnx can be evaluated by using integration by parts. The…

Q: Find ☆ f'(x) using using derivative rules. f(x) =Dx+ 2 to 11

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Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: Given function, fx=e-x a=-0.1 Formula for the linearization at x=a is given by Lx=fa+f'ax-a

Q: Find the derivative off with respect to x of f(x) = In x⁹. The derivative off with respect to x of…

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Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

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Q: Find Tn cebtered at x=0 fir akk b for the function f(x) = 1/(1+x) at a=0

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Q: Find f'(x) (the derivative of f(x)) if f(x) = 7x'3 - 2x'2 + 4x - %3D 5. O 21x^2 - 4x + 4 + C O 21x^2…

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