NDA 2010
- Exam
- NDA
- Year
- 2010
- Subject
- Mathematics
- Chapter
- Differentiation
NDA 2010 · Mathematics · Differentiation
What is the derivative of ^2 x with respect to ^2 x ?
What is the derivative of with respect to ?
Options
- A
- B
- C-1
- D1
Correct answer
C. -1
Step-by-step solution
\begin{aligned} & \text{ Let } u=\sin ^2 x \\ & \text{and } v=\cos ^2 x \\ & \begin{aligned} \therefore \frac{d u}{d x} & =2 \sin x \cdot \cos x \\ \frac{d u}{d x} & =-2 \cos x \cdot \sin x \\ \therefore \quad \frac{d u}{d v} & =\frac{d u}{d x} \times \frac{d x}{d v} \\ & =\frac{2 \sin x \cdot \cos x}{-2 \sin x \cdot \cos x}=-1\end{aligned}\end{aligned}$