What is the derivative of (4-sqrt(x)^2) ?

The derivative of (4-sqrt(x)^2) is -(4-sqrt(x))/(sqrt(x))

What is the first derivative of (4-sqrt(x)^2) ?

The first derivative of (4-sqrt(x)^2) is -(4-sqrt(x))/(sqrt(x))

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\frac{d}{d x} ((4 - x)^{2})

- \frac{4 - x}{x}

Solution steps

\frac{d}{d x} ((4 - x)^{2})

Apply the chain rule:

2 (4 - x) \frac{d}{d x} (4 - x)

= 2 (4 - x) \frac{d}{d x} (4 - x)

\frac{d}{d x} (4 - x) = - \frac{1}{2 x}

= 2 (4 - x) (- \frac{1}{2 x})

Simplify

2 (4 - x) (- \frac{1}{2 x}) : - \frac{4 - x}{x}

= - \frac{4 - x}{x}

\int \frac{100}{25 + ( 5 y ) ^{2}} + e^{4} d y

\frac{y ( 4 x + 4 y )}{( x ^{2} + y ^{2} )}

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What is the derivative of (4-sqrt(x)^2) ?
The derivative of (4-sqrt(x)^2) is -(4-sqrt(x))/(sqrt(x))
What is the first derivative of (4-sqrt(x)^2) ?
The first derivative of (4-sqrt(x)^2) is -(4-sqrt(x))/(sqrt(x))