Practice question · Select all that apply
Select every derivative below that is computed CORRECTLY.
Hints
- Two options break a specific rule the lesson names; check each against the product rule and the constant rule.
- For x times e^x, both factors depend on x.
Show the answer
- A. The derivative of (2x + 5)^3 is 6(2x + 5)^2
- D. The derivative of x^4 is 4x^3
- E. The derivative of 5x^2 is 10x
Why
The product rule gives (x e^x)' = e^x + x e^x, not e^x alone, and the derivative of a constant is 0. The composition (2x + 5)^3 correctly picks up the inner factor 2, giving 3(2x + 5)^2 times 2 = 6(2x + 5)^2.
Practise Differentiation Rules
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