What is the derivative of 2^{ln(x}) ?

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

What is the first derivative of 2^{ln(x}) ?

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

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\frac{d}{d x} (2^{l n (x)})

\frac{ln ( 2 )}{x ^{- l n (2) + 1}}

Solution steps

\frac{d}{d x} (2^{l n (x)})

Apply exponent rule:

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

2^{l n (x)} = e^{l n (x) l n (2)}

= \frac{d}{d x} (e^{l n (x) l n (2)})

Apply the chain rule:

e^{l n (x) l n (2)} \frac{d}{d x} (ln (x) ln (2))

= e^{l n (x) l n (2)} \frac{d}{d x} (ln (x) ln (2))

\frac{d}{d x} (ln (x) ln (2)) = \frac{ln ( 2 )}{x}

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

Simplify

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

= \frac{ln ( 2 )}{x ^{- l n (2) + 1}}

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