CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY3 Marks
Question
If $\text{y}=\text{x}+\tan\text{x},$ show that $\cos^2\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}-2\text{y}+2\text{x}=0$
✓
Answer
$\text{y}=\text{x}+\tan\text{x},$ differentiating w.r.t.x, we get $\Rightarrow\frac{\text{dy}}{\text{dx}}=1+\sec^2\text{x}$ differentiating w.r.t.x, we get $\Rightarrow\frac{\text{d}^2\text{y}}{\text{dx}^2}=0+2\sec^2\times\tan\text{x}$ $\Rightarrow\frac{\text{d}^2\text{y}}{\text{dx}^2}=\frac{2\sin\text{x}}{\cos^3\text{x}}$ $\Rightarrow\cos^2\times\frac{\text{d}^2\text{y}}{\text{dx}^2}=2\tan\text{x}+2\text{x}-2\text{x}$ $\Rightarrow\cos^2\times\frac{\text{d}^2\text{y}}{\text{dx}^2}=2(\text{x}+\tan\text{x})-2\text{x}$ $\Rightarrow\cos^2\times\frac{\text{d}^2\text{y}}{\text{dx}^2}=2\text{y}-2\text{x}$ $\Rightarrow\cos^2\times\frac{\text{d}^2\text{y}}{\text{dx}^2}-2\text{y}+2\text{x}=0$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.