What is the derivative of log_{7}(ln(x)) ?

The derivative of log_{7}(ln(x)) is 1/(ln(7)xln(x))

What is the first derivative of log_{7}(ln(x)) ?

The first derivative of log_{7}(ln(x)) is 1/(ln(7)xln(x))

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\frac{d}{d x} (lo g_{7} (ln (x)))

\frac{1}{ln ( 7 ) x ln ( x )}

Solution steps

\frac{d}{d x} (lo g_{7} (ln (x)))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

= \frac{1}{ln ( 7 )} \cdot \frac{1}{ln ( x )} \cdot \frac{1}{x}

Simplify

\frac{1}{ln ( 7 )} \cdot \frac{1}{ln ( x )} \cdot \frac{1}{x} : \frac{1}{ln ( 7 ) x ln ( x )}

= \frac{1}{ln ( 7 ) x ln ( x )}

\int e^{a r c c o s (x)} d x

\int 2 x - \frac{1}{x ^{2}} d x

\int 2^{x} + x^{2} d x

\frac{\partial}{\partial z} (yz - ln (x + z))

x \to - \infty lim (7)

What is the derivative of log_{7}(ln(x)) ?
The derivative of log_{7}(ln(x)) is 1/(ln(7)xln(x))
What is the first derivative of log_{7}(ln(x)) ?
The first derivative of log_{7}(ln(x)) is 1/(ln(7)xln(x))