What is the derivative of xln(y) ?

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

What is the first derivative of xln(y) ?

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = ln (y)

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

\int - \frac{4}{3}

\frac{\partial}{\partial x} (2 x y + y)

\int_{0}^{1} \frac{x - x}{7} d x

\int 2 ln (x) x d x

\int_{0}^{16} 4 x - x d x

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