What is the derivative of log_{3}(sin(x)) ?

The derivative of log_{3}(sin(x)) is (cot(x))/(ln(3))

What is the first derivative of log_{3}(sin(x)) ?

The first derivative of log_{3}(sin(x)) is (cot(x))/(ln(3))

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\frac{d}{d x} (lo g_{3} (sin (x)))

\frac{cot ( x )}{ln ( 3 )}

Solution steps

\frac{d}{d x} (lo g_{3} (sin (x)))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( sin ( x ) )}{ln ( 3 )})

Take the constant out:

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

= \frac{1}{ln ( 3 )} \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 ( 3 )} \cdot \frac{1}{sin ( x )} cos (x)

Simplify

\frac{1}{ln ( 3 )} \cdot \frac{1}{sin ( x )} cos (x) : \frac{cot ( x )}{ln ( 3 )}

= \frac{cot ( x )}{ln ( 3 )}

\int 5 x ln (1 + x) d x

x^{2}, x

\frac{d}{d x} (8 sin (8 x))

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

f (x) = \frac{x}{x ^{2} + 7}

What is the derivative of log_{3}(sin(x)) ?
The derivative of log_{3}(sin(x)) is (cot(x))/(ln(3))
What is the first derivative of log_{3}(sin(x)) ?
The first derivative of log_{3}(sin(x)) is (cot(x))/(ln(3))