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)

Q.

Find the derivative of:

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

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

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

Q. Find the derivative of:
$\left(i\right)$ $2x-\frac{3}{4}$
$\left(ii\right)$ $(5x^3+3x-1)(x-1)$
$\left(iii\right)$ $x^{-3}(5+3x)$
$\left(iv\right)$ $\left(x^5\right)(3-6x^{-9})$
$\left(v\right)$ $\left(x^{-4}\right)(3-4x^{-5})$
$\left(vi\right)$ $\frac{2}{x+1}-\frac{x^2}{3x-1}$

Q.

Question 24
Factorise
(i) $2x^3–3x^2–17x+30$

(ii) $x^3–6x^2+11x–6$

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

(iv) $3x^3–x^2-3x+1$

Q. Which of the following are quadratic equations?

(i) x² + 6x − 4 = 0
(ii) $\sqrt{3}{x}^2-2x+\frac{1}{2}=0$
(iii) $x^2+\frac{1}{x^2}=5$
(iv) $x-\frac{3}{x}=x^2$
(v) $2x^2-\sqrt{3x}+9=0$
(vi) $x^2-2x-\sqrt{x}-5=0$
(vii) 3x² − 5x + 9 = x² − 7x + 3
(viii) $x+\frac{1}{x}=1$
(ix) x² − 3x = 0
(x) ${\left(x+\frac{1}{x}\right)}^2=3\left(x+\frac{1}{x}\right)+4$
(xi) (2x + 1) (3x + 2) = 6(x − 1) (x − 2)
(xii) $x+\frac{1}{x}=x^2,x\ne 0$
(xiii) 16x² − 3 = (2x + 5) (5x − 3)
(xiv) (x + 2)³ = x³ − 4
(xv) x(x + 1) + 8 = (x + 2) (x − 2)

Q.

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)