What is the derivative of 4^{ln(x}) ?

The derivative of 4^{ln(x}) is 2ln(2)x^{2ln(2)-1}

What is the first derivative of 4^{ln(x}) ?

The first derivative of 4^{ln(x}) is 2ln(2)x^{2ln(2)-1}

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\frac{d}{d x} (4^{l n (x)})

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

Solution steps

\frac{d}{d x} (4^{l n (x)})

Apply exponent rule:

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

4^{l n (x)} = e^{l n (x) l n (4)}

= \frac{d}{d x} (e^{l n (x) l n (4)})

Apply the chain rule:

e^{l n (x) l n (4)} \frac{d}{d x} (ln (x) ln (4))

= e^{l n (x) l n (4)} \frac{d}{d x} (ln (x) ln (4))

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

= e^{l n (x) l n (4)} \frac{2 ln ( 2 )}{x}

Simplify

e^{l n (x) l n (4)} \frac{2 ln ( 2 )}{x} : 2 ln (2) x^{2 l n (2) - 1}

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

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What is the derivative of 4^{ln(x}) ?
The derivative of 4^{ln(x}) is 2ln(2)x^{2ln(2)-1}
What is the first derivative of 4^{ln(x}) ?
The first derivative of 4^{ln(x}) is 2ln(2)x^{2ln(2)-1}