en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^{15x}

Solution

\frac{d}{d x} (x^{15 x})

Solution

15 x^{15 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} (x^{15 x})

Apply exponent rule:

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

x^{15 x} = e^{15 x l n (x)}

= \frac{d}{d x} (e^{15 x l n (x)})

Apply the chain rule:

e^{15 x l n (x)} \frac{d}{d x} (15 x ln (x))

= e^{15 x l n (x)} \frac{d}{d x} (15 x ln (x))

\frac{d}{d x} (15 x ln (x)) = 15 (ln (x) + 1)

= e^{15 x l n (x)} \cdot 15 (ln (x) + 1)

e^{15 x l n (x)} = x^{15 x}

= 15 x^{15 x} (ln (x) + 1)

Graph

Popular Examples

integral of (6x)/((x-5)^2)

\int \frac{6 x}{( x - 5 ) ^{2}} d x

limit as x approaches 2 of sqrt(6x^2+1)

x \to 2 lim (6 x^{2} + 1)

integral from-infinity to 0 of e^{9x}

\int_{- \infty}^{0} e^{9 x} d x

t^2((dy)/(dt))+4ty-y^3=0

t^{2} (\frac{d y}{d t}) + 4 t y - y^{3} = 0

slope of x^3+y^3-6xy=0,(4/3 , 8/3)slope

x^{3} + y^{3} - 6 x y = 0, (\frac{4}{3}, \frac{8}{3})

Frequently Asked Questions (FAQ)

What is the derivative of x^{15x} ?
The derivative of x^{15x} is 15x^{15x}(ln(x)+1)
What is the first derivative of x^{15x} ?
The first derivative of x^{15x} is 15x^{15x}(ln(x)+1)