10) Find the derivatives of the following functions a) y = In√x²-7 -7- b) Use logarithmic differentiation: y = e4x +1 c) f(x) = ln e²x+1 x³√√5x-3 (x-2)²

Q: 4) Find the derivative from FIRST PRINCIPLES of √(x) = 2√x (You will need to rationalize the…

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Q: a) Use Logarithmic differentiation to take derivative of y = f(x) = (x)ª cos² x (x3+1)3

A: We use Logarithmic properties

Q: 7. Find the following derivatives. a) In(x² + 1) dx c) y = 4log3 (x²) b) E = 25,000.101.5M d) Use…

A: Find the derivative.

Q: Activity 1: Use the Rules of Differentiation to differentiate the following functions: a. f(x) = 2x³…

A: We can solve subpart a,c& e as below.

Q: Match each function to the rule you would need to use to compute its derivative. Answers may be used…

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Q: Find the derivative of each function. Show all your work and simplify the result completely.…

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

Q: Jse logarithmic differentiation 14) = ル r+1 y%3D Vx2-4

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Q: (b) g(x):= 1/x for x E R, x#0, (d) k(x):= 1//x for x > 0.

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Q: a) y = (3x²-7) 5 (x²+x)9 7x b) x= c²² Sin²x (x²_qx+5)³ C) y = (Sinx) Sin - ² x 3

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Q: Exercise 2: Derive the formula for the derivative of arcsec(x) in two different ways: (a) Let…

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Q: a) A function is given below with unknown coefficients B and C: f(x) = x³ - 6x² + Bx + C i) Find the…

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Q: What is the derivative of y = log b( cos² (ax)) ? Note that a and b are real numbers.

A: we have to find derivative

Q: 3. a) Use the Chain Rule and the fact that |x| = Vx2 to show that d dx |x| b) Sketch the graphs of…

A: We will use the give solution as we are instructed.

Q: y = (x+6)(x+8)® (x+3)³(x+5)5 Differentiate using Logarithmic Differentiation

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Q: Find the derivative. 4. y = 3x 6x - 7

A: Given  y=3x4+6x3+7 To take derivative , we apply power rule for each term  ddxan=nan-1 Derivative of…