Question 39 of 70intermediate🔧 ApplyShort Answer6 marks

Find the derivative of

(i)

2x−342x - \frac{3}{4}

Answer

2

(ii)

(5x3+3x−1)(x−1)(5x^3 + 3x - 1)(x - 1)

Answer

20x320x^{3} - 15x215x^{2} + 6x - 4

(iii)

x−3(5+3x)x^{-3}(5 + 3x)

Answer

-15x−415x^{-4} - 6x−36x^{-3}

(iv)

x5(3−6x−9)x^5(3 - 6x^{-9})

Answer

15x415x^{4} + 24x−524x^{-5}

(v)

x−4(3−4x−5)x^{-4}(3 - 4x^{-5})

Answer

-12x−512x^{-5} + 36x−1036x^{-10}

(vi)

2x+1−x23x−1\frac{2}{x + 1} - \frac{x^2}{3x - 1}

Answer

−2(x+1)2−3x2−2x(3x−1)2\frac{-2}{(x+1)^2} - \frac{3x^2 - 2x}{(3x-1)^2}

Explanation

This question tests application of derivative rules: sum/difference rule, product rule, and quotient rule. The context shows examples of quotient rule in Example 15 and product rule in Example 18. For polynomial terms, use the power rule: derivative of xnx^{n} is nx^(n-1).

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