What is the derivative of x^{x^3} ?

The derivative of x^{x^3} is x^{x^3}(3x^2ln(x)+x^2)

What is the first derivative of x^{x^3} ?

The first derivative of x^{x^3} is x^{x^3}(3x^2ln(x)+x^2)

Popular >

derivative of

x^{x^{3}}

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})

f (x) =, 4 at x

\frac{d}{d y} (6 y^{2})

\frac{d}{d x} (x + 3 y^{\frac{1}{3}})

y = \frac{x ^{3}}{x - 1}

\frac{\partial}{\partial x} (y e^{x} + sin (y))

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