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TMUA 2020 · Paper 1 · Question 1 of 20

TMUA 2020 Paper 1 Question 1

Differentiation and integration — Differentiation · simplify to powers of x first. Try it first; the answer and a full worked solution are below.

TMUA 2020 · Paper 1Differentiation and integrationDifferentiation · simplify to powers of x first6 options
Which of the following is an expression for the first derivative with respect to x of x3 − 5x22x√x
  1. A−√x2
  2. B√x4
  3. C3x − 54√x
  4. D3√x − 54√x
  5. E3√x − 103√x
  6. F3x2 − 10x3√x
Show the answer and worked solution
answer · C
  1. A−√x2
  2. B√x4
  3. C3x − 54√x
  4. D3√x − 54√x
  5. E3√x − 103√x
  6. F3x2 − 10x3√x
Do not reach for the quotient rule. The denominator is 2x3/2, so the expression is 12(x3/2 − 5x1/2). Differentiating term by term gives 12(32 x1/2 − 52 x−1/2) = 34√x − 54√x. Putting that over the common denominator 4√x gives 3x − 54√x.