What is the derivative of f(x)=x^{4x} ?

The derivative of f(x)=x^{4x} is 4x^{4x}(ln(x)+1)

What is the first derivative of f(x)=x^{4x} ?

The first derivative of f(x)=x^{4x} is 4x^{4x}(ln(x)+1)

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derivative of

f (x) = x^{4 x}

4 x^{4 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} (x^{4 x})

Apply exponent rule:

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

x^{4 x} = e^{4 x l n (x)}

= \frac{d}{d x} (e^{4 x l n (x)})

Apply the chain rule:

e^{4 x l n (x)} \frac{d}{d x} (4 x ln (x))

= e^{4 x l n (x)} \frac{d}{d x} (4 x ln (x))

\frac{d}{d x} (4 x ln (x)) = 4 (ln (x) + 1)

= e^{4 x l n (x)} \cdot 4 (ln (x) + 1)

e^{4 x l n (x)} = x^{4 x}

= 4 x^{4 x} (ln (x) + 1)

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What is the derivative of f(x)=x^{4x} ?
The derivative of f(x)=x^{4x} is 4x^{4x}(ln(x)+1)
What is the first derivative of f(x)=x^{4x} ?
The first derivative of f(x)=x^{4x} is 4x^{4x}(ln(x)+1)