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Derivative of One Function w.r.t Another

Find the deri...

Question

Find the derivative of

(i) (ii) (5x³ + 3x – 1) (x – 1)

(iii) x^–3 (5 + 3x) (iv) x⁵ (3 – 6x^–9)

(v) x^–4 (3 – 4x^–5) (vi)

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Solution

(i) Let

(ii) Let f (x) = (5x³ + 3x – 1) (x – 1)

By Leibnitz product rule,

(iii) Let f (x) = x^{– 3} (5 + 3x)

By Leibnitz product rule,

(iv) Let f (x) = x⁵ (3 – 6x^–9)

By Leibnitz product rule,

(v) Let f (x) = x^–4 (3 – 4x^–5)

By Leibnitz product rule,

(vi) Let f (x) =

By quotient rule,

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Similar questions

Find the derivative of:

(i) 2x - $\frac{3}{4}$
(ii) $(5 x^{3} + 3 x - 1)$ (x-1)

(iii) $x^{- 3}$ (5+3x)
(iv) $x^{5} (3 - 6 x^{- 9})$

(v) $x^{- 4} (3 - 4 x^{- 5})$
(vi) $\frac{2}{x + 1} - \frac{x^{2}}{3 x - 1}$

Q. Which of the following are quadratic equations?

(i) x² + 6x − 4 = 0
(ii)

\sqrt{3} x^{2} - 2 x + \frac{1}{2} = 0

x^{2} + \frac{1}{x^{2}} = 5

x - \frac{3}{x} = x^{2}

2 x^{2} - \sqrt{3 x} + 9 = 0

x^{2} - 2 x - \sqrt{x} - 5 = 0

(vii) 3x² − 5x + 9 = x² − 7x + 3
(viii)

x + \frac{1}{x} = 1

(ix) x² − 3x = 0
(x)

{(x + \frac{1}{x})}^{2} = 3 (x + \frac{1}{x}) + 4

(xi) (2x + 1) (3x + 2) = 6(x − 1) (x − 2)
(xii)

x + \frac{1}{x} = x^{2}, x \neq 0

(xiii) 16x² − 3 = (2x + 5) (5x − 3)
(xiv) (x + 2)³ = x³ − 4
(xv) x(x + 1) + 8 = (x + 2) (x − 2)

Question 24
Factorise
(i) $2 x^{3} - 3 x^{2} - 17 x + 30$

(ii) $x^{3} - 6 x^{2} + 11 x - 6$

(iii) $x^{3} + x^{2} - 4 x - 4$

(iv) $3 x^{3} - x^{2} - 3 x + 1$

Use the identity (x + a) (x + b) = x² + (a + b)x + ab to find the following products.

(i) (x + 3) (x + 7) (ii) (4x +5) (4x + 1)

(iii) (4x − 5) (4x − 1) (iv) (4x + 5) (4x − 1)

(v) (2x +5y) (2x + 3y) (vi) (2a² +9) (2a² + 5)

(vii) (xyz − 4) (xyz − 2)

Solve the equations:

(i) 5x = 3x + 24;

(ii) 8t + 5 = 2t − 31;

(iii) 7x − 10 = 4x + 11;

(iv) 4z + 3 = 6 + 2z;

(v) 2x − 1 = 14 − x;

(vi) 6x + 1 = 3(x − 1) + 7;

(vii) ;

(viii) ;

(ix) 3(x + 1) = 12 + 4 (x − 1);

(x) 2x − 5 = 3(x − 5);

(xi) 6(1 − 4x) + 7(2 + 5x) = 53;

(xii) 3(x + 6) + 2 (x + 3) = 64;

(xiii) ;

(xiv) .

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