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

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

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

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

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

\int \frac{9 + u}{u} d u

\int \frac{u}{u ^{2} - 1} d u

\frac{\partial}{\partial x} (sin (4 x - 6 y))

f (x) = 6 sin (2 x) - 3 cos (3 x)

y^{^{''}} - y = t e^{t}

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