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DIAGNOSTIC TEST

This diagnostic test focuses on derivatives and antiderivatives in calculus. It covers functions such as ( f(x) = x cos x ) and ( f(x) = sin^3 x ), testing your knowledge on the rules of differentiation like the product rule and that of trigonometric functions. You'll encounter questions addressing common misconceptions, such as derivative formulas. Each question provides immediate feedback, encouraging a deeper understanding of calculus while reinforcing correct principles. Complete the test to assess your calculus skills!

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DIAGNOSTIC TEST

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  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’ • Click here to continue • Click here to try again

  4. Wrong! • The derivative of cos x is – sin x, not sin x • Click here to continue • Click here to try again

  5. Correct! • Great job!

  6. 2. The derivative of f(x) = is

  7. Wrong! • The derivative of is • Click here to continue • Click here to try again

  8. Correct! • Great job!

  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 • Click here to continue • Click here to try again

  11. Correct! • Great job!

  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 • Click here to continue • Click here to try again

  14. Correct! • Great job!

  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 • Click here to continue • Click here to try again

  17. Correct! • Great job!

  18. CONGRATULATION! YOU ARE DONE!

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