What is the derivative of log_{5}(tan(x)) ?

The derivative of log_{5}(tan(x)) is (sec^2(x))/(ln(5)tan(x))

What is the first derivative of log_{5}(tan(x)) ?

The first derivative of log_{5}(tan(x)) is (sec^2(x))/(ln(5)tan(x))

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\frac{d}{d x} (lo g_{5} (tan (x)))

\frac{sec ^{2} ( x )}{ln ( 5 ) tan ( x )}

Solution steps

\frac{d}{d x} (lo g_{5} (tan (x)))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( tan ( x ) )}{ln ( 5 )})

Take the constant out:

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

= \frac{1}{ln ( 5 )} \frac{d}{d x} (ln (tan (x)))

Apply the chain rule:

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

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

\frac{d}{d x} (tan (x)) = sec^{2} (x)

= \frac{1}{ln ( 5 )} \cdot \frac{1}{tan ( x )} sec^{2} (x)

Simplify

\frac{1}{ln ( 5 )} \cdot \frac{1}{tan ( x )} sec^{2} (x) : \frac{sec ^{2} ( x )}{ln ( 5 ) tan ( x )}

= \frac{sec ^{2} ( x )}{ln ( 5 ) tan ( x )}

x \to 4 - lim (c x^{2} + 3 x)

\int 2 x^{3} - 20 x^{- 5} d x

n = 0 \sum \infty \frac{2 ^{n}}{8 ^{n}}

\frac{d}{d x} (4 x + \frac{3}{x})

\frac{e ^{- s}}{s ^{2} + 1}

What is the derivative of log_{5}(tan(x)) ?
The derivative of log_{5}(tan(x)) is (sec^2(x))/(ln(5)tan(x))
What is the first derivative of log_{5}(tan(x)) ?
The first derivative of log_{5}(tan(x)) is (sec^2(x))/(ln(5)tan(x))