I rewrote the quesion

y = sqrt (4 + sin 10x)

change it to

y = (4+sin10x)^(1/2)
so
dy/dx = (1/2)(4+sin10x)^(-1/2)(10cos10x)
= 5cos10x /(4+sin10x)^(1/2)
= 5cos10x /√(4+sin10x)

To rewrite the equation y = sqrt(4 + sin(10x)), you can apply the inverse operation to both sides of the equation.

1. Start with the given equation: y = sqrt(4 + sin(10x)).
2. Square both sides of the equation to eliminate the square root: y^2 = 4 + sin(10x).
3. Subtract 4 from both sides of the equation to isolate sin(10x): y^2 - 4 = sin(10x).

Therefore, the rewritten equation is y^2 - 4 = sin(10x).

The given expression is y = √(4 + sin(10x)).

To understand this expression, we first need to understand the individual components:

1. sin(10x): This represents the sine of 10x. The sine function calculates the ratio of the length of the side opposite to a given angle to the length of the hypotenuse in a right triangle. In this case, the angle is 10x.

2. 4 + sin(10x): Here, we add 4 to the result of sin(10x).

3. √(4 + sin(10x)): Lastly, we take the square root of the sum obtained above.

Now, if you have a specific question related to this expression, please let me know and I'll do my best to help you further.