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

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

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

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

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

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

Solution steps

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

Simplify

(6 x)^{6 x} : 4665 6^{x} x^{6 x}

= \frac{d}{d x} (4665 6^{x} x^{6 x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 4665 6^{x}, g = x^{6 x}

= \frac{d}{d x} (4665 6^{x}) x^{6 x} + \frac{d}{d x} (x^{6 x}) 4665 6^{x}

\frac{d}{d x} (4665 6^{x}) = ln (6) \cdot 6^{6 x + 1}

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

= ln (6) \cdot 6^{6 x + 1} x^{6 x} + 6 x^{6 x} (ln (x) + 1) \cdot 4665 6^{x}

6 x^{6 x} (ln (x) + 1) \cdot 4665 6^{x} = 6^{1 + 6 x} x^{6 x} (ln (x) + 1)

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

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