Question
Differentiate the following function with respect to x:
$\text{x}^{-4}(3-\text{4x}^{-5})$
$\text{x}^{-4}(3-\text{4x}^{-5})$
Then, $\text{u}'=-\text{4x}^{-5};\text{v}'=\text{20x}^{-6}$
Using the product rule:
$\frac{\text{d}}{\text{dx}}(\text{uv})=\text{uv}'+\text{vu}'$
$\frac{\text{d}}{\text{dx}}[\text{x}^{-4}(3-\text{4x}^{-5})]=\text{x}^{-4}(\text{20x}^{-6})+(3-\text{4x}^{-5})(-\text{4x}^{-5})$
$=\text{20x}^{-10}-\text{12x}^{-5}+\text{16x}^{-10}$
$=-\text{12x}^{-5}+\text{36x}^{-10}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Find the middle term in the expansion of:
$\Big(\frac{2}{3}\text{x}-\frac{3}{2\text{x}}\Big)^{20}$
| Age (In years) | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 |
| Number of Persons | 3 | 61 | 132 | 153 | 140 | 51 | 2 |