What is the derivative of ln(sqrt(x)+7) ?

The derivative of ln(sqrt(x)+7) is 1/(2sqrt(x)(\sqrt{x)+7)}

What is the first derivative of ln(sqrt(x)+7) ?

The first derivative of ln(sqrt(x)+7) is 1/(2sqrt(x)(\sqrt{x)+7)}

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\frac{d}{d x} (ln (x + 7))

\frac{1}{2 x ( x + 7 )}

Solution steps

\frac{d}{d x} (ln (x + 7))

Apply the chain rule:

\frac{1}{x + 7} \frac{d}{d x} (x + 7)

= \frac{1}{x + 7} \frac{d}{d x} (x + 7)

\frac{d}{d x} (x + 7) = \frac{1}{2 x}

= \frac{1}{x + 7} \cdot \frac{1}{2 x}

Simplify

\frac{1}{x + 7} \cdot \frac{1}{2 x} : \frac{1}{2 x ( x + 7 )}

= \frac{1}{2 x ( x + 7 )}

\frac{d}{d x} (3^{t a n (x)})

\frac{d y}{d x} = \frac{y ^{2} + 2 x y}{x ^{2}}

\int \frac{1 - 2 x}{x ( 1 - x )} d x

\frac{- 4 x}{x ^{2} + 1}

\frac{d}{d x} ((x - 4)^{2})

What is the derivative of ln(sqrt(x)+7) ?
The derivative of ln(sqrt(x)+7) is 1/(2sqrt(x)(\sqrt{x)+7)}
What is the first derivative of ln(sqrt(x)+7) ?
The first derivative of ln(sqrt(x)+7) is 1/(2sqrt(x)(\sqrt{x)+7)}