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Popular >

derivative of x^{x^4}

Solution

\frac{d}{d x} (x^{x^{4}})

Solution

x^{x^{4}} (4 x^{3} ln (x) + x^{3})

Solution steps

\frac{d}{d x} (x^{x^{4}})

Apply exponent rule:

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

x^{x^{4}} = e^{x^{4} l n (x)}

= \frac{d}{d x} (e^{x^{4} l n (x)})

Apply the chain rule:

e^{x^{4} l n (x)} \frac{d}{d x} (x^{4} ln (x))

= e^{x^{4} l n (x)} \frac{d}{d x} (x^{4} ln (x))

\frac{d}{d x} (x^{4} ln (x)) = 4 x^{3} ln (x) + x^{3}

= e^{x^{4} l n (x)} (4 x^{3} ln (x) + x^{3})

e^{x^{4} l n (x)} = x^{x^{4}}

= x^{x^{4}} (4 x^{3} ln (x) + x^{3})

Popular Examples

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

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

y^{^{''}} = x

y^'+4/3 y=1-1/4 t

y^{^{'}} + \frac{4}{3} y = 1 - \frac{1}{4} t

integral from-1 to 0 of 3(e^{1/x})/(x^3)

\int_{- 1}^{0} 3 \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

derivative of 1/pi sin(pix)

\frac{d}{d x} (\frac{1}{π} sin (π x))

Frequently Asked Questions (FAQ)

What is the derivative of x^{x^4} ?
The derivative of x^{x^4} is x^{x^4}(4x^3ln(x)+x^3)
What is the first derivative of x^{x^4} ?
The first derivative of x^{x^4} is x^{x^4}(4x^3ln(x)+x^3)