What is the derivative of log_{10}(sin(x)) ?

The derivative of log_{10}(sin(x)) is (cot(x))/(ln(10))

What is the first derivative of log_{10}(sin(x)) ?

The first derivative of log_{10}(sin(x)) is (cot(x))/(ln(10))

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\frac{d}{d x} (lo g_{10} (sin (x)))

\frac{cot ( x )}{ln ( 10 )}

Solution steps

\frac{d}{d x} (lo g_{10} (sin (x)))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( sin ( x ) )}{ln ( 10 )})

Take the constant out:

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

= \frac{1}{ln ( 10 )} \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 ( 10 )} \cdot \frac{1}{sin ( x )} cos (x)

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{sin ( x )} cos (x) : \frac{cot ( x )}{ln ( 10 )}

= \frac{cot ( x )}{ln ( 10 )}

x \to - 4 lim (5 x + 20 - 8)

\int \frac{1}{2} (x + \frac{1}{2} sin (2 x)) d x

x \to 1 lim (x^{2} - 2 x)

\frac{\partial}{\partial y} (x^{2} - 5 x y + 3 y^{2})

x \to - 2 lim ((2 x - 1)^{2})

What is the derivative of log_{10}(sin(x)) ?
The derivative of log_{10}(sin(x)) is (cot(x))/(ln(10))
What is the first derivative of log_{10}(sin(x)) ?
The first derivative of log_{10}(sin(x)) is (cot(x))/(ln(10))