What is the derivative of y=x^{5^x} ?

The derivative of y=x^{5^x} is x^{5^x}(ln(5)*5^xln(x)+(5^x)/x)

What is the first derivative of y=x^{5^x} ?

The first derivative of y=x^{5^x} is x^{5^x}(ln(5)*5^xln(x)+(5^x)/x)

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derivative of

y = x^{5^{x}}

x^{5^{x}} (ln (5) \cdot 5^{x} ln (x) + \frac{5 ^{x}}{x})

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

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

\int \frac{1}{64 e ^{- 5 x} + e ^{5 x}} d x

θ \to 0 lim (cot (π θ))

x \to 8 lim (\frac{f ( x )}{g ( x )})

\frac{d}{d x} (\frac{4}{1 - 9 x})

What is the derivative of y=x^{5^x} ?
The derivative of y=x^{5^x} is x^{5^x}(ln(5)*5^xln(x)+(5^x)/x)
What is the first derivative of y=x^{5^x} ?
The first derivative of y=x^{5^x} is x^{5^x}(ln(5)*5^xln(x)+(5^x)/x)