Using the first principle of derivative: f(x + Ax) – f(x) f'(x) = lim Ax-0 Ax 3 Differentiate: f(x) = 3/x squarred O+3/x squarred O 3/x O 1/x

Q: 3. Approximate the first order derivative of f(x)= x² + 2x at x = 3, using Forward, Backward and…

A: Formulas for differences are enclosed next page

Q: Derivative of In |x| Differentiate In x, for x > 0, and differentiate In(-x), for x < 0, to conclude…

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Q: f(x+Ax)- f(x) Using the first principle of derivative f'(x) = %3D Ax Ax-0 Differentiate: y 4x - 6

A: Derivative of the function

Q: Find the derivative of the function by the limit process. Find an equation of the tangent line to…

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Q: 2. Using the definition of derivative, prove the following: (a) f= if so)=V (b) y-sec x if y-tanx

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Q: ©if g(x, v) = In(),the )If g(x, y) = Int then xgx - vgw in simplified form is [c].

A: We can find the answer as below in the following steps

Q: Find the derivative by the limit process. f(x) = 15 – x2 Step 1 Complete the definition of a…

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Q: 5 Find the derivative of f with respect to x of f(x) = In x°. 5 The derivative of f with respect to…

A: Given,  f(x)=lnx5we have to find the derivative of f with respect to x

Q: 5y + xy-

A: Differentiation: 5y+xy-4=0 ddx(uv)=udvdx+vdudx ddx(y)=dydx

Q: Using the (limit) definition of derivative to show that the derivative of the function sin(x) is…

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Q: central-difference method to approximate the derivative of f(x) = ln x² with value Use of x at 1.8,…

A: As multiple questions are there and it is not mentioned that which question to be solved, I will…

Q: using the equation f(x)= x^2+x find slope of tangent line f′(2) using the limit definition of a…

A: The slope of the tangent is given by f'(x). We will use the limit formula to find f'(x)…

Q: ) Prove that tanh'x = tn/itx, X€ (-1,1) i) , Sinh 'x and tanh'x Find the derivative of coch'x

A: (1). We have to prove that:   tanh-1x=12ln1+x1-x

Q: Find the approximate derivative for f(x) = cos x on the interval [-7, 1] using forward difference…

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Q: 4. Find the derivative of the function using the definition of derivative. State the domain of the…

A: f'(x) = limh→0 f(x+h)-f(x)h. The domain of the function is the set of all possible input values for…

Q: (8) Find the derivative of the functions (i)h(x) = sin 2.x cos 2x (ii) f (x) = cos (tan 4.x) 1 =-…

A: We need to differentiate the given function. We will use different method of differentiation . ( As…

Q: Using the limit definition of derivative, compute the derivative of the following function. No…

A: by limit definition of derivativesf'(x) =limn→0 f(x+h)-f(x)hf(x) = 3x2-2xf(x+h) = 3(x+h)2- 2(x+h)

Q: Using limit definition of derivative, prove d/dx e^x=e^x

A: We using limit definition

Q: 6. Using the limit defenition of the derivative, find the equation of the line tangent to the curve…

A: We have to find the slope of the tangent line at first.Then we find its equation.

Q: Find the derivative of y = tan 1 1-x -1 + sec Va +1

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Q: Using the fact that u(x) = In u(x) – In v(x), In v(x) use the chain rule and the formula for the…

A: lnu(x)v(x)=ln u(x)-ln v(x)Formula:ddxln f(x)=1f(x)f'(x)

Q: Fi id the derivative using Chain rule. Ln X+3

A: Please see the explanation below..

Q: 4. Find the derivative of f(x) = Vr +1 using the limit definition. (a) Find the slope of the tangent…

A: (1) The derivative from the limit definition is:…

Q: FINAL EXAM Page 2 of 28 Previous Next If f(x) = 4x² +8x + 5, find f' (x) using the limit definition…

A: We have to find derivative.

Q: using the derivative definition how do I find f(x) = -6(square root over x).

A: The limit definition is on the board . First we find f(x+h) amd substitute the value in the limit…

Q: True of False: Derivative of (arctan(e^(-x^2))) = [-2xe^(-x^2)] / [1 + e^(-2x^2)] Show your…

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Q: Using Chain Rule method Find the derivative of: 5 2. F= x³ + x² + x + 1 1. F(x) = ln Cos(x²)

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Q: 4) Use the Chain Rule instead of the Quotient Rule. 4 Find the derivative y= 2x +1

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Q: 17. f(x) = x2 + x – 3

A: Answer is f'(x)= 2x+1. Explanation is given below using the limit process....

Q: sinh x O Compute the derivative of f(x) = (cosh x)

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Q: (x+ Ax)-S(x) Use the definition of the derivative f'(x) = lim Ax0 to find the equation of the line…

A: Use definition of derivative

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

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Q: 9 f:(-0,0) U (0, ∞) → (∞,0) U (0, ∞0). Where f(x) х Show that f(x) is continuous at x=3 with the…

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Q: Using chain rule, find the derivative of the hyperbolic functions: f(x) = tanh(4x) f (x) = In…

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Q: f(x+Ax)-f(x) Use the definition of the derivative f'(x) = lim Ax-0 to find the equation of the line…

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Q: Using the fact that In[u(x)v(x)] = In u(x) + In v(x), use the chain rule and the formula for the…

A: Given: lnuxvx=lnux+lnvxddxlnx=1x

Q: Use the definition of the derivative to compute the derivative of the function f(x) = 1 – 6x² at an…

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Q: Find the derivative of a function at a given point F(x)= 2e^x-x at x=1 F(x)= x^3-5x at x=2

A: We have to find derivatives of the function: Fx=2ex-x at x=1 and Fx=x3-5x at x=2. We know the…

Q: How do you prove the general power rule of derivatives using the inverse property (x^n=e^(nlnx))?

A: The general power rule:

Q: se the limit definition of the derivative to find the slope of the tangent line to the curve f ( x )…

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Q: Find the derivative at the given x-value. Show your work! 2n * f(x) = 3 tanx at x = : f(x) = 2 sec x…

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Q: Using terms like "secant line" and "tangent line", explain how evaluating f(3+ h) – f(3) lim gives…

A: This is a problem related to derivation of the general formula of differentiation.

Q: Find the derivative of y 3 sin x +5 cos x A. 3 cos x +5 sin x C. 5 cos x +3 sin x B. 3 cos x-5 sin x…

A: Differentiate wrt x

Q: 5. Calculate the derivative of x* sin (x) showing all your work. 6. Use the limit definition of the…

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Q: 5. f(x) = 3-5x+ x use limit definition of derivative)

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Q: Find an equation of the tangent line to the graph of y = f ( x ) at the point on the graph where x…

A: The slope of the tangent line of a graph y = f(x) at a point x0 is given by the derivative of…

Q: Using differentiation rule, find the derivative of the function ƒ (²) = [2 + (² ² + 1)²³ at _z = 1 +…

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Q: Find the derivative of: a. f(x)=ln(csc^2(x)) b. f(x)=ln|sec(5x)+tan(5x)| c. f(x)=(lnx^2)^2

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Q: Find the derivative of a composite function using the Chain Rule or General Power Rule.  1.)…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…