What is the derivative of (5^x)^x ?

The derivative of (5^x)^x is 2ln(5)*5^{x^2}x

What is the first derivative of (5^x)^x ?

The first derivative of (5^x)^x is 2ln(5)*5^{x^2}x

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derivative of

(5^{x})^{x}

2 ln (5) \cdot 5^{x^{2}} x

Solution steps

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

Simplify

(5^{x})^{x} : 5^{x^{2}}

= \frac{d}{d x} (5^{x^{2}})

Apply exponent rule:

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

5^{x^{2}} = e^{x^{2} l n (5)}

= \frac{d}{d x} (e^{x^{2} l n (5)})

Apply the chain rule:

e^{x^{2} l n (5)} \frac{d}{d x} (x^{2} ln (5))

= e^{x^{2} l n (5)} \frac{d}{d x} (x^{2} ln (5))

\frac{d}{d x} (x^{2} ln (5)) = 2 ln (5) x

= e^{x^{2} l n (5)} \cdot 2 ln (5) x

e^{x^{2} l n (5)} = 5^{x^{2}}

= 2 ln (5) \cdot 5^{x^{2}} x

(\frac{( a + x )}{( a - x )})^{\frac{3}{2}}

\frac{d}{d p} (20 - p)

∣ x + 2 ∣ - 1

\frac{a}{x ^{2}}

y = 6 x - 3

What is the derivative of (5^x)^x ?
The derivative of (5^x)^x is 2ln(5)*5^{x^2}x
What is the first derivative of (5^x)^x ?
The first derivative of (5^x)^x is 2ln(5)*5^{x^2}x