KC Sinha Mathematics Solution Class 12 Chapter 11 अवकलन (Differentiation) Exercise 11.1 (Q9-Q12)

Exercise 11.1

Question 9

cos(sin x³)

Question 10

$\sin \sqrt{1+x^{2}}$
Sol :
Let y=$\sin \sqrt{1+x^{2}}$

Differentiating with respect to x

$\frac{d y}{dx}=\frac{d(\sin \sqrt{1+x^{2}})}{d(\sqrt{1+x^{2}})} \times \frac{d(\sqrt{1+x^{2}})}{d\left(1+x^{2}\right)} \times \frac{d\left(1+x^{2}\right)}{dx}$

$=\cos \sqrt{1+x^{2}} \cdot \frac{1}{2 \sqrt{1+x^{2}}} \times 2 x$

$=\frac{x}{\sqrt{1+x^{2}}} \cos \sqrt{1+x^{2}}$

Question 11

$\sqrt{\tan 2 x}$
Sol :
Let y=$\sqrt{\tan 2 x}$

Differentiating with respect to x

$\frac{d y}{d x}=\frac{d(\sqrt{\tan 2 x})}{d(\tan 2 x)} \times \frac{d(\tan 2 x)}{d(2 x)} \times \frac{d(2 x)}{d x}$

$=\frac{1}{2 \sqrt{\tan 2 x}} \times \sec ^{2} 2 x \cdot 2$

$=\frac{\sec ^{2} 2 x}{\sqrt{\tan 2 x}}$

Question 12

$\sqrt{\sin x^{2}}$
Sol :
Let y=$\sqrt{\sin x^{2}}$

Differentiating with respect to x

$\frac{d y}{d x}=\frac{d(\sqrt{\sin x^{2}})}{d\left(\sin x^{2}\right)}-\frac{d\left(\sin x^{2}\right)}{d\left(x^{2}\right)} \times \frac{d\left(x^{2}\right)}{d x}$

$=\frac{1}{2 \sqrt{\sin x^{2}}} \times \cos x^{2} \times 2 x$

$=\frac{x \cos x^{2}}{\sqrt{\sin x^{2}}}$