What is the derivative of yln(x) ?

The derivative of yln(x) is ln(x)(dy)/(dx)+y/x

What is the first derivative of yln(x) ?

The first derivative of yln(x) is ln(x)(dy)/(dx)+y/x

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = ln (x)

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

\frac{1}{x} y = \frac{y}{x}

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

What is the derivative of yln(x) ?
The derivative of yln(x) is ln(x)(dy)/(dx)+y/x
What is the first derivative of yln(x) ?
The first derivative of yln(x) is ln(x)(dy)/(dx)+y/x