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

The derivative of (cos(x)/(log_{3)(x)}) is (-xsin(x)ln(x)-cos(x))/(ln(3)xlog_{3)(x)^2}

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

The first derivative of (cos(x)/(log_{3)(x)}) is (-xsin(x)ln(x)-cos(x))/(ln(3)xlog_{3)(x)^2}

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\frac{d}{d x} (\frac{cos ( x )}{lo g _{3} ( x )})

\frac{- x sin ( x ) ln ( x ) - cos ( x )}{ln ( 3 ) x lo g _{3} ( x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{cos ( x )}{lo g _{3} ( x )})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( cos ( x ) ) lo g _{3} ( x ) - \frac{d}{d x} ( lo g _{3} ( x ) ) cos ( x )}{( lo g _{3} ( x ) ) ^{2}}

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

\frac{d}{d x} (lo g_{3} (x)) = \frac{1}{x ln ( 3 )}

= \frac{( - sin ( x ) ) lo g _{3} ( x ) - \frac{1}{x l n ( 3 )} cos ( x )}{( lo g _{3} ( x ) ) ^{2}}

Simplify

\frac{( - sin ( x ) ) lo g _{3} ( x ) - \frac{1}{x l n ( 3 )} cos ( x )}{lo g _{3} ( x ) ^{2}} : \frac{- x sin ( x ) ln ( x ) - cos ( x )}{ln ( 3 ) x lo g _{3} ( x ) ^{2}}

= \frac{- x sin ( x ) ln ( x ) - cos ( x )}{ln ( 3 ) x lo g _{3} ( x ) ^{2}}

\int \frac{x}{4 x ^{2} + 5} d x

\frac{\partial}{\partial x} (\frac{r x ( K ( r , x ) - x )}{K ( r , x ) + a x})

f (x) = 3 x^{2} + 1

y^{^{'}} = \frac{( 4 t + y )}{4 y - t}

5 3 x^{3} + x

What is the derivative of (cos(x)/(log_{3)(x)}) ?
The derivative of (cos(x)/(log_{3)(x)}) is (-xsin(x)ln(x)-cos(x))/(ln(3)xlog_{3)(x)^2}
What is the first derivative of (cos(x)/(log_{3)(x)}) ?
The first derivative of (cos(x)/(log_{3)(x)}) is (-xsin(x)ln(x)-cos(x))/(ln(3)xlog_{3)(x)^2}