What is the derivative of ln(x+y+5) ?

The derivative of ln(x+y+5) is (\frac{dy)/(dx)+1}{x+y+5}

What is the first derivative of ln(x+y+5) ?

The first derivative of ln(x+y+5) is (\frac{dy)/(dx)+1}{x+y+5}

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\frac{d}{d x} (ln (x + y + 5))

\frac{\frac{d y}{d x} + 1}{x + y + 5}

Solution steps

\frac{d}{d x} (ln (x + y + 5))

Apply the chain rule:

\frac{1}{x + y + 5} \frac{d}{d x} (x + y + 5)

= \frac{1}{x + y + 5} \frac{d}{d x} (x + y + 5)

\frac{d}{d x} (x + y + 5) = \frac{d y}{d x} + 1

= \frac{1}{x + y + 5} (\frac{d y}{d x} + 1)

Simplify

\frac{1}{x + y + 5} (\frac{d y}{d x} + 1) : \frac{\frac{d y}{d x} + 1}{x + y + 5}

= \frac{\frac{d y}{d x} + 1}{x + y + 5}

\int \frac{1}{200 - x} d x

\frac{d y}{d t} + e^{t} y = - 18 e^{t}

\frac{d}{d x} (4 + 4 x)

\frac{x ^{2}}{x + 2}

sin^{2} (e^{s i n^{2} (t)})

What is the derivative of ln(x+y+5) ?
The derivative of ln(x+y+5) is (\frac{dy)/(dx)+1}{x+y+5}
What is the first derivative of ln(x+y+5) ?
The first derivative of ln(x+y+5) is (\frac{dy)/(dx)+1}{x+y+5}