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Popular >

derivative of ln(x+ln(y))

Solution

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

Solution

\frac{y + x \frac{d y}{d x}}{x y}

Solution steps

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

Simplify

ln (x) + ln (y) : ln (x y)

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{y + x \frac{d y}{d x}}{x y}

Popular Examples

(\partial)/(\partial x)(y^2zln(1+x^2))

\frac{\partial}{\partial x} (y^{2} z ln (1 + x^{2}))

derivative of y=cos^{ln(7x)}(x)derivative of

y = cos^{l n (7 x)} (x)

integral of 1/(sin(x)-cos(x)-1)

\int \frac{1}{sin ( x ) - cos ( x ) - 1} d x

integral from 0 to 7/3 of sqrt(9+3x)

\int_{0}^{\frac{7}{3}} 9 + 3 x d x

(\partial)/(\partial x)(log_{e}(x^2+y^2))

\frac{\partial}{\partial x} (lo g_{e} (x^{2} + y^{2}))

Frequently Asked Questions (FAQ)

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