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

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

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

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

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

- \frac{tan ( x )}{ln ( 10 )}

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{tan ( x )}{ln ( 10 )}

n = 0 \sum \infty n^{3} (x - 5)^{n}

\frac{d y}{d x} 7 x^{3} + 7 y^{3} - 3 x y = 0

\frac{d}{d x} (\frac{5 x - 7}{6 x - 9})

\int x^{14} e^{x^{15}} d x

\int \frac{3}{4} d x

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