What is the derivative of (5x^3^x) ?

The derivative of (5x^3^x) is (ln(5x^3)+3)(5x^3)^x

What is the first derivative of (5x^3^x) ?

The first derivative of (5x^3^x) is (ln(5x^3)+3)(5x^3)^x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} ((5 x^{3})^{x})

(ln (5 x^{3}) + 3) (5 x^{3})^{x}

Solution steps

\frac{d}{d x} ((5 x^{3})^{x})

Apply exponent rule:

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

(5 x^{3})^{x} = e^{x l n (5 x^{3})}

= \frac{d}{d x} (e^{x l n (5 x^{3})})

Apply the chain rule:

e^{x l n (5 x^{3})} \frac{d}{d x} (x ln (5 x^{3}))

= e^{x l n (5 x^{3})} \frac{d}{d x} (x ln (5 x^{3}))

\frac{d}{d x} (x ln (5 x^{3})) = ln (5 x^{3}) + 3

= e^{x l n (5 x^{3})} (ln (5 x^{3}) + 3)

e^{x l n (5 x^{3})} = (5 x^{3})^{x}

= (ln (5 x^{3}) + 3) (5 x^{3})^{x}

What is the derivative of (5x^3^x) ?
The derivative of (5x^3^x) is (ln(5x^3)+3)(5x^3)^x
What is the first derivative of (5x^3^x) ?
The first derivative of (5x^3^x) is (ln(5x^3)+3)(5x^3)^x