What is the derivative of sqrt((x^2(y^2-9))) ?

The derivative of sqrt((x^2(y^2-9))) is (y^2-9+xy\frac{dy)/(dx)}{sqrt(y^2-9)}

What is the first derivative of sqrt((x^2(y^2-9))) ?

The first derivative of sqrt((x^2(y^2-9))) is (y^2-9+xy\frac{dy)/(dx)}{sqrt(y^2-9)}

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\frac{d}{d x} ((x^{2}) (y^{2} - 9))

\frac{y ^{2} - 9 + x y \frac{d y}{d x}}{y ^{2} - 9}

Solution steps

\frac{d}{d x} ((x^{2}) (y^{2} - 9))

Apply the chain rule:

\frac{1}{2 x ^{2} ( y ^{2} - 9 )} \frac{d}{d x} (x^{2} (y^{2} - 9))

= \frac{1}{2 x ^{2} ( y ^{2} - 9 )} \frac{d}{d x} (x^{2} (y^{2} - 9))

\frac{d}{d x} (x^{2} (y^{2} - 9)) = 2 x (y^{2} - 9) + 2 y \frac{d y}{d x} x^{2}

= \frac{1}{2 x ^{2} ( y ^{2} - 9 )} (2 x (y^{2} - 9) + 2 y \frac{d y}{d x} x^{2})

Simplify

\frac{1}{2 x ^{2} ( y ^{2} - 9 )} (2 x (y^{2} - 9) + 2 y \frac{d y}{d x} x^{2}) : \frac{y ^{2} - 9 + x y \frac{d y}{d x}}{y ^{2} - 9}

= \frac{y ^{2} - 9 + x y \frac{d y}{d x}}{y ^{2} - 9}

What is the derivative of sqrt((x^2(y^2-9))) ?
The derivative of sqrt((x^2(y^2-9))) is (y^2-9+xy\frac{dy)/(dx)}{sqrt(y^2-9)}
What is the first derivative of sqrt((x^2(y^2-9))) ?
The first derivative of sqrt((x^2(y^2-9))) is (y^2-9+xy\frac{dy)/(dx)}{sqrt(y^2-9)}