What is the derivative of log_{10}(1+cos(x)) ?

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

What is the first derivative of log_{10}(1+cos(x)) ?

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

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\frac{d}{d x} (lo g_{10} (1 + cos (x)))

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

Solution steps

\frac{d}{d x} (lo g_{10} (1 + cos (x)))

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 + cos (x)) = - sin (x)

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

Simplify

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

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

\frac{d}{d x} (ln (\frac{7}{x ^{2} - x + 2}))

y^{^{''}} - 8 y^{^{'}} + 13 y = 0, y (0) = 0, y^{^{'}} (0) = 5

\int_{- \infty}^{0} x e^{9 x} d x

\frac{\partial}{\partial y} (y^{3} - y)

f (x) = x^{2} - 8

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