Practice question · Sort into groups
Sort each claimed derivative as correct or incorrect.
Groups: Correct · Incorrect
- d/dx of sin(x squared) is cos(x squared)
- d/dx of (x times sin x) is cos x
- d/dx of x to the fifth is 5x to the fourth
- The exponential function is its own derivative
Hints
- Any composite expression needs the inner derivative attached; check those first.
- For the quotient, the numerator is 1 times (x + 1) minus x times 1.
Show the answer
Correct: d/dx of x to the fifth is 5x to the fourth, The exponential function is its own derivative
Incorrect: d/dx of sin(x squared) is cos(x squared), d/dx of (x times sin x) is cos x
Why
Items 2 and 5 both drop an inner derivative, of 2 in each case. Item 4 is correct: the quotient rule gives ((x + 1) - x) over (x + 1) squared = 1/(x + 1) squared. Item 6 is correct too, since (1/x squared) times 2x = 2/x, the chain rule was applied and simplified.
Practise Differentiation Rules
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