What is the derivative of x^{log_{6}(x}) ?

The derivative of x^{log_{6}(x}) is (2x^{log_{6}(x)-1}ln(x))/(ln(6))

What is the first derivative of x^{log_{6}(x}) ?

The first derivative of x^{log_{6}(x}) is (2x^{log_{6}(x)-1}ln(x))/(ln(6))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (x^{l o g_{6} (x)})

\frac{2 x ^{l o g_{6} (x) - 1} ln ( x )}{ln ( 6 )}

Solution steps

\frac{d}{d x} (x^{l o g_{6} (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{l o g_{6} (x)} = e^{l o g_{6} (x) l n (x)}

= \frac{d}{d x} (e^{l o g_{6} (x) l n (x)})

Apply the chain rule:

e^{l o g_{6} (x) l n (x)} \frac{d}{d x} (lo g_{6} (x) ln (x))

= e^{l o g_{6} (x) l n (x)} \frac{d}{d x} (lo g_{6} (x) ln (x))

\frac{d}{d x} (lo g_{6} (x) ln (x)) = \frac{2 ln ( x )}{ln ( 6 ) x}

= e^{l o g_{6} (x) l n (x)} \frac{2 ln ( x )}{ln ( 6 ) x}

Simplify

e^{l o g_{6} (x) l n (x)} \frac{2 ln ( x )}{ln ( 6 ) x} : \frac{2 x ^{l o g_{6} (x) - 1} ln ( x )}{ln ( 6 )}

= \frac{2 x ^{l o g_{6} (x) - 1} ln ( x )}{ln ( 6 )}

\int - 6 cos (x) d x

\int 11 ln (x^{2} - x + 2) d x

\frac{( e ^{x} + e ^{- x} )}{2}

y^{^{'}} - 2 t y = 4 t^{3}

\int_{4}^{5} x 25 - x^{2} d x

What is the derivative of x^{log_{6}(x}) ?
The derivative of x^{log_{6}(x}) is (2x^{log_{6}(x)-1}ln(x))/(ln(6))
What is the first derivative of x^{log_{6}(x}) ?
The first derivative of x^{log_{6}(x}) is (2x^{log_{6}(x)-1}ln(x))/(ln(6))