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

The derivative of sqrt(y^2-x) is (2y\frac{dy)/(dx)-1}{2sqrt(y^2-x)}

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

The first derivative of sqrt(y^2-x) is (2y\frac{dy)/(dx)-1}{2sqrt(y^2-x)}

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

\frac{2 y \frac{d y}{d x} - 1}{2 y ^{2} - x}

Solution steps

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

Apply the chain rule:

\frac{1}{2 y ^{2} - x} \frac{d}{d x} (y^{2} - x)

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

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

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

Simplify

\frac{1}{2 y ^{2} - x} (2 y \frac{d y}{d x} - 1) : \frac{2 y \frac{d y}{d x} - 1}{2 y ^{2} - x}

= \frac{2 y \frac{d y}{d x} - 1}{2 y ^{2} - x}

What is the derivative of sqrt(y^2-x) ?
The derivative of sqrt(y^2-x) is (2y\frac{dy)/(dx)-1}{2sqrt(y^2-x)}
What is the first derivative of sqrt(y^2-x) ?
The first derivative of sqrt(y^2-x) is (2y\frac{dy)/(dx)-1}{2sqrt(y^2-x)}