What is the derivative of (x^2^{2x}) ?

The derivative of (x^2^{2x}) is 2x^{4x}(2ln(x)+2)

What is the first derivative of (x^2^{2x}) ?

The first derivative of (x^2^{2x}) is 2x^{4x}(2ln(x)+2)

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

2 x^{4 x} (2 ln (x) + 2)

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

e^{2 x l n (x^{2})} \cdot 2 (ln (x^{2}) + 2) : 2 x^{4 x} (2 ln (x) + 2)

= 2 x^{4 x} (2 ln (x) + 2)

What is the derivative of (x^2^{2x}) ?
The derivative of (x^2^{2x}) is 2x^{4x}(2ln(x)+2)
What is the first derivative of (x^2^{2x}) ?
The first derivative of (x^2^{2x}) is 2x^{4x}(2ln(x)+2)