1. DIAGNOSTIC TEST
CALCULUS 2
MATH 208

2. 1. The derivative of f(x) = x cosx is
1 sin x
cos x + x sin x
cos x - x sin x
-1 sinx

3. Wrong! The derivative of uv is (uv)’ = u’v+uv’ NOT u’v’
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4. Wrong! The derivative of cos x is – sin x, not sin x
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5. Correct!
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6. 2. The derivative of f(x) = is

7. Wrong! The derivative of is Click here to continue
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8. Correct!
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9. 3. The derivative of f(x) = sin3x is
3 sin x cos x
-3 sin2x cos x
3 sin2x cos x
3 sin2 x

10. Wrong! The derivative of un is (un)’ = nun-1u’ and
The derivative of sin x is cos x, not – cos x
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11. Correct!
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12. 4. An antiderivative of x2+ sec2 x is
2x + 2sec2x tan x
x3/3 + tan x
x3/3 - tan x

13. Wrong! The derivative of x2 is 2x, the antiderivative is x3/3
The antiderivative of sec2x is tanx
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14. Correct!
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15. 5. The integral (x5 – cos 2x)dx is
5x4 - 2sin 2x
x5/5 + (sin 2x)/2
x5/5 – 2 sin 2x
x5/5 – (sin 2x)/2

16. Wrong! The derivative of x5 is 5x4, the antiderivative is x5/5
The antiderivative of cos nx is (sin nx)/n
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17. Correct!
Great job!

18. CONGRATULATION!
YOU ARE DONE!