What is the derivative of 1/(log_{2(x)}) ?

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

What is the first derivative of 1/(log_{2(x)}) ?

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

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\frac{d}{d x} (\frac{1}{lo g _{2} ( x )})

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

Solution steps

\frac{d}{d x} (\frac{1}{lo g _{2} ( x )})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{1}{3} tan^{3} (x))

f (x) = \frac{x ^{2} + 4}{x ^{2} - 4}

\int \frac{( 1 - x ^{2} )}{x} d x

f (x) = 5 x^{2} - 8 x + 3, at x = 1

x \to 0 lim (tan (\frac{x}{2}))

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