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

The derivative of log_{10}(arcsin(cos(x))) is -1/(ln(10)arcsin(cos(x)))

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

The first derivative of log_{10}(arcsin(cos(x))) is -1/(ln(10)arcsin(cos(x)))

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\frac{d}{d x} (lo g_{10} (arcsin (cos (x))))

- \frac{1}{ln ( 10 ) arcsin ( cos ( x ) )}

Solution steps

\frac{d}{d x} (lo g_{10} (arcsin (cos (x))))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( arcsin ( cos ( x ) ) )}{ln ( 10 )})

Take the constant out:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (arcsin (cos (x))))

Apply the chain rule:

\frac{1}{arcsin ( cos ( x ) )} \frac{d}{d x} (arcsin (cos (x)))

= \frac{1}{arcsin ( cos ( x ) )} \frac{d}{d x} (arcsin (cos (x)))

\frac{d}{d x} (arcsin (cos (x))) = - csc (x) sin^{2} (x)

= \frac{1}{ln ( 10 )} \cdot \frac{1}{arcsin ( cos ( x ) )} (- csc (x) sin^{2} (x))

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{arcsin ( cos ( x ) )} (- csc (x) sin^{2} (x)) : - \frac{1}{ln ( 10 ) arcsin ( cos ( x ) )}

= - \frac{1}{ln ( 10 ) arcsin ( cos ( x ) )}

\int \frac{sin ( 2 x )}{15 + cos ^{2} ( x )} d x

\int \frac{10}{x ^{2} - 1} d x

y = x^{\frac{1}{2}}, y = x - 2, [0, 4]

\frac{( s + 1 )}{( s ^{2} + 2 s + 2 )}

cos^{3} (t)

What is the derivative of log_{10}(arcsin(cos(x))) ?
The derivative of log_{10}(arcsin(cos(x))) is -1/(ln(10)arcsin(cos(x)))
What is the first derivative of log_{10}(arcsin(cos(x))) ?
The first derivative of log_{10}(arcsin(cos(x))) is -1/(ln(10)arcsin(cos(x)))