en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of y=x^{x^3}

Solution

derivative of

y = x^{x^{3}}

Solution

x^{x^{3}} (3 x^{2} ln (x) + x^{2})

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{3} ln (x)) = 3 x^{2} ln (x) + x^{2}

= e^{x^{3} l n (x)} (3 x^{2} ln (x) + x^{2})

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

= x^{x^{3}} (3 x^{2} ln (x) + x^{2})

Graph

Popular Examples

integral of (4x^2+4x)/(2x-1)

\int \frac{4 x ^{2} + 4 x}{2 x - 1} d x

integral of (2e^x)/(sqrt(1-e^{2x))}

\int \frac{2 e ^{x}}{1 - e ^{2 x}} d x

derivative of 9x^2sin(x)tan(x)

d er i v a t i v e 9 x^{2} sin (x) tan (x)

integral of acos(t)

\int a cos (t) d t

(dy)/(dx)=(5(3-y)^2)/((3-x)^2)

\frac{d y}{d x} = \frac{5 ( 3 - y ) ^{2}}{( 3 - x ) ^{2}}

Frequently Asked Questions (FAQ)

What is the derivative of y=x^{x^3} ?
The derivative of y=x^{x^3} is x^{x^3}(3x^2ln(x)+x^2)
What is the first derivative of y=x^{x^3} ?
The first derivative of y=x^{x^3} is x^{x^3}(3x^2ln(x)+x^2)