Limits and Derivatives — MATHS STD 11 Science — Question

1. sin⁡ x + tan⁡ x sec⁡ x

Solution:

We follow product rule $\frac{\text{d}}{\text{dx}}(\text{f}.\text{g})=\text{g.}\frac{\text{d}}{\text{dx}}(\text{f})+(\text{f})\frac{\text{d}}{\text{dx}}(\text{f}.\text{g})$

Here, f = sin⁡ x and g = tan⁡ x

$\frac{\text{d}}{\text{dx}}$ (sin⁡ x tan⁡ x) = cos⁡ x tan⁡ x + sec²⁡ x sinx

$\frac{\text{d}}{\text{dx}}$ (sin⁡ x tan⁡ x) = sin⁡ x + tan⁡ x sec⁡ x