I can't solve this problem, can anyone help me
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[tex]\red{\rule{50pt}{3pt}}\blue{\rule{50pt}{3pt}}\orange{\rule{50pt}{3pt}}\green{\rule{50pt}{3pt}}\pink{\rule{50pt}{3pt}}\color{maroon}{\rule{50pt}{3pt}}[/tex][tex]\huge \color{lime} \boxed{ \colorbox{black}{answer}}[/tex]
Sure, let's break it down step by step. First, let's differentiate the numerator and denominator separately.
For the numerator:
Let's call the first term √(a+x) and the second term √(a-x). The derivative of √(a+x) with respect to x is (1/2)(a+x)^(-1/2), and the derivative of √(a-x) with respect to x is (-1/2)(a-x)^(-1/2).
For the denominator:
Let's call the first term √(a+x) and the second term √(a-x). The derivative of √(a+x) with respect to x is (1/2)(a+x)^(-1/2), and the derivative of √(a-x) with respect to x is (-1/2)(a-x)^(-1/2).
Now, let's apply the quotient rule. The quotient rule states that if y = u/v, then dy/dx = (v * du/dx - u * dv/dx) / v^2.
Substituting the derivatives we found earlier, we have:
dy/dx = ((√(a+x) - √(a-x)) * (1/2)(a+x)^(-1/2) - (√(a+x) + √(a-x)) * (-1/2)(a-x)^(-1/2)) / (√(a+x) - √(a-x))^2.
Simplifying further, we get:
dy/dx = ((a+x) - (a-x)) / ((a+x) - (a-x)) * (1/2)(a+x)^(-1/2)(a-x)^(-1/2).
Now, we can simplify it even more:
dy/dx = (2x) / (2√(a+x)√(a-x)).
So, the derivative dy/dx is equal to (2x) / (2√(a+x)√(a-x)).
[tex]\huge{\color{black}{\color{white}{\textbf{\textsf{ \underline{\underline{\colorbox{black}{Answer࿐}}}}}}}}[/tex]
For the numerator:
Let's call the first term √(a+x) and the second term √(a-x). The derivative of √(a+x) with respect to x is (1/2)(a+x)^(-1/2), and the derivative of √(a-x) with respect to x is (-1/2)(a-x)^(-1/2).
For the denominator:
Let's call the first term √(a+x) and the second term √(a-x). The derivative of √(a+x) with respect to x is (1/2)(a+x)^(-1/2), and the derivative of √(a-x) with respect to x is (-1/2)(a-x)^(-1/2).
Now, let's apply the quotient rule. The quotient rule states that if y = u/v, then dy/dx = (v * du/dx - u * dv/dx) / v^2.
Substituting the derivatives we found earlier, we have:
dy/dx = ((√(a+x) - √(a-x)) * (1/2)(a+x)^(-1/2) - (√(a+x) + √(a-x)) * (-1/2)(a-x)^(-1/2)) / (√(a+x) - √(a-x))^2.
Simplifying further, we get:
dy/dx = ((a+x) - (a-x)) / ((a+x) - (a-x)) * (1/2)(a+x)^(-1/2)(a-x)^(-1/2).
Now, we can simplify it even more:
dy/dx = (2x) / (2√(a+x)√(a-x)).
So, the derivative dy/dx is equal to (2x) / (2√(a+x)√(a-x)).
☆ Hope it's helpful ☆