QuestionFind $\frac{d y}{d x}$ for $y=\sin x-\cos 3 x$ at $x=45^{\circ}$.

Studdy Solution
Finally, we can calculate the value of the derivative at $x=45^{\circ}$$$\frac{d y}{d x} \bigg|_{x=45^{\circ}} = \frac{1}{\sqrt{2}} +3 \times \frac{1}{\sqrt{2}} =4 \times \frac{1}{\sqrt{2}}$$So, $\frac{d y}{d x} \bigg|_{x=45^{\circ}} =4 \times \frac{1}{\sqrt{2}}$.