What is the derivative of f(x)=x^{6x} ?

The derivative of f(x)=x^{6x} is 6x^{6x}(ln(x)+1)

What is the first derivative of f(x)=x^{6x} ?

The first derivative of f(x)=x^{6x} is 6x^{6x}(ln(x)+1)

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derivative of

f (x) = x^{6 x}

6 x^{6 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} (x^{6 x})

Apply exponent rule:

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

x^{6 x} = e^{6 x l n (x)}

= \frac{d}{d x} (e^{6 x l n (x)})

Apply the chain rule:

e^{6 x l n (x)} \frac{d}{d x} (6 x ln (x))

= e^{6 x l n (x)} \frac{d}{d x} (6 x ln (x))

\frac{d}{d x} (6 x ln (x)) = 6 (ln (x) + 1)

= e^{6 x l n (x)} \cdot 6 (ln (x) + 1)

e^{6 x l n (x)} = x^{6 x}

= 6 x^{6 x} (ln (x) + 1)

What is the derivative of f(x)=x^{6x} ?
The derivative of f(x)=x^{6x} is 6x^{6x}(ln(x)+1)
What is the first derivative of f(x)=x^{6x} ?
The first derivative of f(x)=x^{6x} is 6x^{6x}(ln(x)+1)