Tutor profile: Stephanie O.
Find the derivative of the following function: f(x) = x^2 + 2x^5 + 20
1. Use the chain rule, where: if f(x) = x^n (where n is any constant), then the derivative f'(x) = n*x^(n-1) 2. solve for the derivative, f'(x) by taking the derivative of each term in f(x) f'(x) = 2x + 10x^4 **Remember that the derivative of a constant equals 0
Identify the subject and the predicate in the following sentences: 1. The sun was shining brightly. 2. The dogs were barking loudly. 3. The pretty girl was wearing a blue frock. 4. My younger brother serves in the army. 5. The man and his wife were working in their garden. 6. My mother and my aunt are trained classical dancers. 7. You don’t have to wait for me. 8. We will no longer tolerate this. 9. The little tree was covered with needles instead of leaves. 10. A rich merchant was passing by the shoemaker’s window.
1. The sun (subject) / was shining brightly (predicate). 2. The dogs (subject) / were barking loudly (predicate). 3. The pretty girl (subject) / was wearing a blue frock (predicate). 4. My younger brother (subject) / serves in the army (predicate). 5. The man and his wife (subject) / were working in their garden (predicate). 6. My mother and my aunt (subject) / are trained classical dancers (predicate). 7. You (subject) / don’t have to wait for me (predicate). 8. We (subject) / will no longer tolerate this (predicate). 9. The little tree (subject) / was covered with needles instead of leaves (predicate). 10. A rich merchant (subject) /was passing by the shoemaker’s window (predicate).
Solve for X: 10x + 2(x+7) = 20x + 5
1. Begin by simplifying the expression and expanding the "2(x+7)" term: 2(x+7) ---> 2x + 14 2. Rewrite the original expression with the expanded "2(x+7)" term: 10x + 2(x+7) = 20x + 5 10x + 2x + 14 = 20x + 5 3. Combine like terms on both sides: 12x + 14 = 20x + 5 4. Get all the x's on one side and the constant terms on the other by adding/subtracting: 12x + 14 = 20x + 5 ---> *subtract 12x from both sides* 12x - 12x + 14 = 20x - 12x + 5 14 = 8x + 5 ---> subtract 5 from both sides 14 - 5 = 8x + 5 - 5 9 = 8x 5. Divide both sides by 8 to isolate (solve for) x: x = 9/8
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