Question

# Differentiate the following with respect to the variable: y=2\sin 50

Derivatives
Differentiate the following with respect to the variable: $$\displaystyle{y}={2}{\sin{{50}}}$$

2021-05-04
Step 1
Given that:
$$\displaystyle{y}={2}{\sin{{50}}}$$
Step 2
Apply chain rule of derivatives,
Differentiating  w.r.t.θ
$$\displaystyle{y}'={\frac{{{d}}}{{{d}{0}}}}{\left({2}{\sin{{\left({50}\right)}}}\right)}$$
$$\displaystyle={2}{\frac{{{d}}}{{{d}{0}}}}{\sin{{\left({50}\right)}}}$$
$$\displaystyle={2}{\cos{{\left({50}\right)}}}{\frac{{{d}}}{{{d}{0}}}}{50}$$
$$\displaystyle={2}{\cos{{\left({50}\right)}}}\cdot{5}{\left({1}\right)}$$
$$\displaystyle{y}'={10}{\cos{{\left({50}\right)}}}$$