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

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

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

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

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derivative of

f (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}}

6 x^{2} - 9 x - 6, 7 x^{2} - 5 x - 3

x \to 0 lim (\frac{x}{5})

(x^{2} - 9)^{2} + 2

7 x (x + 3 y) y^{^{'}} = 7 y (x - 3 y)

5 \frac{d r}{d s} = e^{r - 8 s}

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