What is the derivative of 43^{sqrt(x)} ?

The derivative of 43^{sqrt(x)} is (ln(43)*43^{sqrt(x)})/(2sqrt(x))

What is the first derivative of 43^{sqrt(x)} ?

The first derivative of 43^{sqrt(x)} is (ln(43)*43^{sqrt(x)})/(2sqrt(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (4 3^{x})

\frac{ln ( 43 ) \cdot 4 3 ^{x}}{2 x}

Solution steps

\frac{d}{d x} (4 3^{x})

Apply exponent rule:

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

4 3^{x} = e^{x l n (43)}

= \frac{d}{d x} (e^{x l n (43)})

Apply the chain rule:

e^{x l n (43)} \frac{d}{d x} (x ln (43))

= e^{x l n (43)} \frac{d}{d x} (x ln (43))

\frac{d}{d x} (x ln (43)) = \frac{ln ( 43 )}{2 x}

= e^{x l n (43)} \frac{ln ( 43 )}{2 x}

Simplify

e^{x l n (43)} \frac{ln ( 43 )}{2 x} : \frac{ln ( 43 ) \cdot 4 3 ^{x}}{2 x}

= \frac{ln ( 43 ) \cdot 4 3 ^{x}}{2 x}

What is the derivative of 43^{sqrt(x)} ?
The derivative of 43^{sqrt(x)} is (ln(43)*43^{sqrt(x)})/(2sqrt(x))
What is the first derivative of 43^{sqrt(x)} ?
The first derivative of 43^{sqrt(x)} is (ln(43)*43^{sqrt(x)})/(2sqrt(x))