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

The derivative of log_{5}(sin(x)) is (cot(x))/(ln(5))

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

The first derivative of log_{5}(sin(x)) is (cot(x))/(ln(5))

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derivative of

lo g_{5} (sin (x))

\frac{cot ( x )}{ln ( 5 )}

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (sin (x)) = cos (x)

= \frac{1}{ln ( 5 )} \cdot \frac{1}{sin ( x )} cos (x)

Simplify

\frac{1}{ln ( 5 )} \cdot \frac{1}{sin ( x )} cos (x) : \frac{cot ( x )}{ln ( 5 )}

= \frac{cot ( x )}{ln ( 5 )}

\int_{\frac{1}{5}}^{3} 4 x ln (5 x) d x

n = 1 \sum \infty \frac{7}{1 0 ^{n}}

f (x) = 2 x^{3} + 36 x^{2} + 192 x + 8

x \to 0 + lim (\frac{e ^{x}}{1 - e ^{- x}})

\frac{d}{d x} (4 e^{6 x})

What is the derivative of log_{5}(sin(x)) ?
The derivative of log_{5}(sin(x)) is (cot(x))/(ln(5))
What is the first derivative of log_{5}(sin(x)) ?
The first derivative of log_{5}(sin(x)) is (cot(x))/(ln(5))