Question

Q5.Solve (sin x + Isinx|)dx​

Answer 1

Solution:

$\dfrac{d}{dx}(sinx + |sinx|) \\\\ = \dfrac{d}{dx}(sinx) + \dfrac{d}{dx}(|sinx|)\\\\= cosx + \dfrac{sinx}{|sinx|} \times \dfrac{d}{dx}(sinx)\\\\= cosx + \dfrac{sinx}{|sinx|} \times cosx \\\\= \dfrac{sinx.cosx}{|sinx|} +cosx$

Formulae Used:

$\dfrac{d}{dx}(x + y) = \dfrac{d}{dx}(x) \times \dfrac{d}{dx}(y)\\\\\dfrac{d}{dx}(sinx) = cosx\\\\\dfrac{d}{dx}(|x|) = \dfrac{x}{|x|}$

Answer 2

Answer:

$\rightarrow\sf\boxed{{{\frac{sin.cosx}{|sinx|}+cosx}}}$

Step-by-step explanation:

$\rightarrow\sf\frac{d}{dx} (sinx + | \: sinx|) \\ \rightarrow\sf \frac{dx}{dx} (sinx) + \frac{d}{dx } (|sinx|) \\ \rightarrow\sf cosx + \frac{sinx}{|sinx|} × \frac{d}{dx} (sinx) \\ \rightarrow\sf cosx + \frac{sinx}{|sinx|} × cosx \\ \rightarrow\sf\boxed{{{\frac{sin.cosx}{|sinx|}+cosx}}}$

✨ Hope it helped! ✨