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Popular >

derivative of x^{x^5}

Solution

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

Solution

x^{x^{5}} (5 x^{4} ln (x) + x^{4})

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{5} ln (x)) = 5 x^{4} ln (x) + x^{4}

= e^{x^{5} l n (x)} (5 x^{4} ln (x) + x^{4})

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

= x^{x^{5}} (5 x^{4} ln (x) + x^{4})

Popular Examples

integral of (-3e^x+4/x)

\int (- 3 e^{x} + \frac{4}{x}) d x

integral from 7 to 8 of e^{7-x}

\int_{7}^{8} e^{7 - x} d x

derivative of sin(2)

\frac{d}{d x} (sin (2))

integral of 2xsqrt(x^2+1)

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

2y^{''}-54y=0,y(1)=1,y(2)=2

2 y^{^{''}} - 54 y = 0, y (1) = 1, y (2) = 2

Frequently Asked Questions (FAQ)

What is the derivative of x^{x^5} ?
The derivative of x^{x^5} is x^{x^5}(5x^4ln(x)+x^4)
What is the first derivative of x^{x^5} ?
The first derivative of x^{x^5} is x^{x^5}(5x^4ln(x)+x^4)