What is the derivative of x^{5x} ?

The derivative of x^{5x} is 5x^{5x}(ln(x)+1)

What is the first derivative of x^{5x} ?

The first derivative of x^{5x} is 5x^{5x}(ln(x)+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

x^{5 x}

5 x^{5 x} (ln (x) + 1)

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (5 x ln (x)) = 5 (ln (x) + 1)

= e^{5 x l n (x)} \cdot 5 (ln (x) + 1)

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

= 5 x^{5 x} (ln (x) + 1)

\int 12 e^{2 t} d t

y = 1 - 4 x, at x = - 1

\int \frac{1}{( 16 x ^{2} + 9 ) ^{2}} d x

\frac{7}{x}, at x = 6

What is the derivative of x^{5x} ?
The derivative of x^{5x} is 5x^{5x}(ln(x)+1)
What is the first derivative of x^{5x} ?
The first derivative of x^{5x} is 5x^{5x}(ln(x)+1)