How to Find the Differential of $y=2\sin^2(x)$ when $x = \pi/4$ and $dx = 0.49$

Question

I am wondering how to find the differential of $y=2\sin^2(x)$ when $x = \pi/4$ and $dx = 0.49$.

I realize that I should be finding the derivative of $y=2\sin^2(x)$, which is $4\sin(x)\cos(x)$. And, I think I should sub $\pi/4$ into the derivative of the equation to get $2$. However, I am not sure what is meant by $dx = 0.49$.

Can anyone please explain what this equation is asking, and how I may find the answer to it?

Answer 1

differencing $y = 2\sin^2 x,$ you get $dy = 4 \sin x \cos x \, dx.$ now subbing $x = \pi/4, dx = 0.49$ gives you $dy = 2 \times 0.49 = 0.98$