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

The derivative of x^{3^x} is x^{3^x}(ln(3)*3^xln(x)+(3^x)/x)

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

The first derivative of x^{3^x} is x^{3^x}(ln(3)*3^xln(x)+(3^x)/x)

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derivative of

x^{3^{x}}

x^{3^{x}} (ln (3) \cdot 3^{x} ln (x) + \frac{3 ^{x}}{x})

Solution steps

\frac{d}{d x} (x^{3^{x}})

Apply exponent rule:

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

x^{3^{x}} = e^{3^{x} l n (x)}

= \frac{d}{d x} (e^{3^{x} l n (x)})

Apply the chain rule:

e^{3^{x} l n (x)} \frac{d}{d x} (3^{x} ln (x))

= e^{3^{x} l n (x)} \frac{d}{d x} (3^{x} ln (x))

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

= e^{3^{x} l n (x)} (ln (3) \cdot 3^{x} ln (x) + \frac{3 ^{x}}{x})

e^{3^{x} l n (x)} = x^{3^{x}}

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

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\frac{d}{d x} (csc (x^{3}))

f (x) = \frac{8 x ^{2} - x + 5}{x + 5}

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