What is the derivative of y= 1/(log_{4)(x)} ?

The derivative of y= 1/(log_{4)(x)} is -1/(2ln(2)xlog_{4)(x)^2}

What is the first derivative of y= 1/(log_{4)(x)} ?

The first derivative of y= 1/(log_{4)(x)} is -1/(2ln(2)xlog_{4)(x)^2}

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derivative of

y = \frac{1}{lo g _{4} ( x )}

- \frac{1}{2 ln ( 2 ) x lo g _{4} ( x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{lo g _{4} ( x )})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} (lo g_{4} (x)^{- 1})

Apply the chain rule:

- \frac{1}{( lo g _{4} ( x ) ) ^{2}} \frac{d}{d x} (lo g_{4} (x))

= - \frac{1}{( lo g _{4} ( x ) ) ^{2}} \frac{d}{d x} (lo g_{4} (x))

\frac{d}{d x} (lo g_{4} (x)) = \frac{1}{2 ln ( 2 ) x}

= - \frac{1}{( lo g _{4} ( x ) ) ^{2}} \cdot \frac{1}{2 ln ( 2 ) x}

Simplify

- \frac{1}{lo g _{4} ( x ) ^{2}} \cdot \frac{1}{2 ln ( 2 ) x} : - \frac{1}{2 ln ( 2 ) x lo g _{4} ( x ) ^{2}}

= - \frac{1}{2 ln ( 2 ) x lo g _{4} ( x ) ^{2}}

\int_{0}^{4} \frac{2}{x ^{2}} d x

\int_{- 1}^{1} 2 x^{2} d x

\frac{d}{d x} (\frac{- 20}{( 2 + x ) ^{2}})

x^{2} - 11, 10 x

(x, y) \to (0, 0) lim (\frac{e ^{x y} - 1}{x y})

What is the derivative of y= 1/(log_{4)(x)} ?
The derivative of y= 1/(log_{4)(x)} is -1/(2ln(2)xlog_{4)(x)^2}
What is the first derivative of y= 1/(log_{4)(x)} ?
The first derivative of y= 1/(log_{4)(x)} is -1/(2ln(2)xlog_{4)(x)^2}