Question7. $\frac{d}{d x}\left[x^{2}\left(x^{3}+7\right)\right]$
8. $\frac{d}{d x}(2 x-3)^{2}$
9. $\frac{d}{d x}\left[\frac{x^{5}+6 x^{4}+5 x^{3}}{x^{2}}\right]$
10. $\frac{d}{d x}\left[\left(3 x^{4}+7\right)\left(x^{3}-5 x\right)\right]$
11. $\frac{d}{d x}\left[\frac{5 x+6}{3 x-7}\right]$
12. $\frac{d}{d x}\left[(7 x+4)\left(x^{2}+8\right)\right]$

Studdy Solution
Differentiate $(7x + 4)(x^2 + 8)$ using the product rule:
Let $u = 7x + 4$ and $v = x^2 + 8$.
Calculate $u'$ and $v'$:
$$u' = \frac{d}{dx}(7x + 4) = 7$$ $$v' = \frac{d}{dx}(x^2 + 8) = 2x$$
Apply the product rule:
$$\frac{d}{dx}[(7x + 4)(x^2 + 8)] = (7)(x^2 + 8) + (7x + 4)(2x)$$
Simplify:
$$= 7x^2 + 56 + 14x^2 + 8x$$ $$= 21x^2 + 8x + 56$$
The derivatives are:
1. $5x^4 + 14x$
2. $8x - 12$
3. $3x^2 + 12x + 5$
4. $21x^6 - 75x^4 + 21x^2 - 35$
5. $\frac{-53}{(3x - 7)^2}$
6. $21x^2 + 8x + 56$