What is the derivative of ln((x+a/(sqrt(y)))) ?

The derivative of ln((x+a/(sqrt(y)))) is (2y-\frac{dy)/(dx)(x+a)}{2(x+a)y}

What is the first derivative of ln((x+a/(sqrt(y)))) ?

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

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\frac{d}{d x} (ln (\frac{x + a}{y}))

\frac{2 y - \frac{d y}{d x} ( x + a )}{2 ( x + a ) y}

Solution steps

\frac{d}{d x} (ln (\frac{x + a}{y}))

Apply the chain rule:

\frac{1}{\frac{x + a}{y}} \frac{d}{d x} (\frac{x + a}{y})

= \frac{1}{\frac{x + a}{y}} \frac{d}{d x} (\frac{x + a}{y})

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

= \frac{1}{\frac{x + a}{y}} \cdot \frac{2 y - \frac{d y}{d x} ( x + a )}{2 y y}

Simplify

\frac{1}{\frac{x + a}{y}} \cdot \frac{2 y - \frac{d y}{d x} ( x + a )}{2 y y} : \frac{2 y - \frac{d y}{d x} ( x + a )}{2 ( x + a ) y}

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

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