Use y - x(x - 5)2 and its derivative dy - 5x(x - 3)(x - 5) to find each of the following. 18 dx 18 Find the critical values. (Enter your answers as a comma-separated list.) Find the critical points. (x, y) = ) (smallest x-value) (х, у) - (x, y) - (largest x-value) Find the intervals on which the function is increasing. (Enter your answer using interval notation.) Find the intervals on which the function is decreasing. (Enter your answer using interval notation.)

Q: y = xe2x

A: We can find the third derivative as below

Q: xy2+5x2-3y2+45=0  (1,5)   Evaluate the derivative at the given function point.

A: We have to find derivative

Q: Find the second derivative. y = 6x3 - 5x2 + 3e* O 10x - 36 + 3e* O 10x - 24 + 3e* O 24x - 10 + 3e* O…

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Q: X(t) = b cos(wt) + V a² – b² sin²(wt)

A: We will use differentiation rules to solve this question.

Q: find the first and second derivatives

A: Given expression: w=3z7-7z3+21z2

Q: Use the quotient rule to find the derivative of the function. y= 3x+1 8x+7 What is the correct way…

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Q: Find the derivative. y = (3x − 3) (3x + 9) None of these 18x² +18x - 81 09 O 18x³ + 18x² - 81x 18x -…

A: The given function is

Q: +7V + - 5x + 6. Find the derivative of y = 9 - 5х + 6.

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Q: 1 EX-1- Find the derivative of the function : f(x)= /2x+3

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Q: 11. In y = e" sin x

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Q: Q2. Find the derivative (the first derivative): a- Y = In (7-2 x 3 )4 Y= (3 x4+9)/(x+5) C- b- 100=…

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Q: Analyze and apply statistics Find the derivative of the following:  a. y = 2x³ - 3x² + 6x – 5…

A: As we know that; The sum difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 The Product rule:…