Question

If $y=\tan (x^{\circ }+{45}^{\circ }),$ then $\frac{dy}{dx}=$

• A. $\frac{\pi }{180}{\sec }^2(x^{\circ }+{45}^{\circ })$
• B. ${\sec }^2(x^{\circ }+{45}^{\circ })$
• C. $\frac{\pi }{180}{\sec }^2(x+{45}^{\circ })$
• D. $\frac{\pi }{4}{\sec }^2(x^{\circ }+{45}^{\circ })$

Answer 1

The correct option is A $\frac{\pi }{180}{\sec }^2(x^{\circ }+{45}^{\circ })$

We have,
$y=\tan (x^{\circ }+{45}^{\circ })$
$y=\tan \left[\right(x+45\left)\frac{\pi }{180}\right]$
$\frac{dy}{dx}={\sec }^2\left[\right(x+45\left)\frac{\pi }{180}\right]\times \frac{d}{dx}\left[\right(x+45\left)\frac{\pi }{180}\right]\text{[using chain rule ]}$
$=\frac{\pi }{180}{\sec }^2(x^{\circ }+{45}^{\circ })$