What is the derivative of (2x^{6x}) ?

The derivative of (2x^{6x}) is 3ln(2)*2^{6x+1}x^{6x}+3*2^{1+6x}x^{6x}(ln(x)+1)

What is the first derivative of (2x^{6x}) ?

The first derivative of (2x^{6x}) is 3ln(2)*2^{6x+1}x^{6x}+3*2^{1+6x}x^{6x}(ln(x)+1)

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\frac{d}{d x} ((2 x)^{6 x})

3 ln (2) \cdot 2^{6 x + 1} x^{6 x} + 3 \cdot 2^{1 + 6 x} x^{6 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} ((2 x)^{6 x})

Simplify

(2 x)^{6 x} : 6 4^{x} x^{6 x}

= \frac{d}{d x} (6 4^{x} x^{6 x})

Apply the Product Rule:

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

f = 6 4^{x}, g = x^{6 x}

= \frac{d}{d x} (6 4^{x}) x^{6 x} + \frac{d}{d x} (x^{6 x}) 6 4^{x}

\frac{d}{d x} (6 4^{x}) = 3 ln (2) \cdot 2^{6 x + 1}

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

= 3 ln (2) \cdot 2^{6 x + 1} x^{6 x} + 6 x^{6 x} (ln (x) + 1) \cdot 6 4^{x}

6 x^{6 x} (ln (x) + 1) \cdot 6 4^{x} = 3 \cdot 2^{1 + 6 x} x^{6 x} (ln (x) + 1)

= 3 ln (2) \cdot 2^{6 x + 1} x^{6 x} + 3 \cdot 2^{1 + 6 x} x^{6 x} (ln (x) + 1)

x \to - \infty lim (x^{2} e^{- 3 x})

x - e^{x}

\int (x - 1)^{- 2} d x

\frac{\partial}{\partial x} (arccos (\frac{x}{y}))

\int sin^{3} (11 x) cos^{2} (11 x) d x

What is the derivative of (2x^{6x}) ?
The derivative of (2x^{6x}) is 3ln(2)*2^{6x+1}x^{6x}+3*2^{1+6x}x^{6x}(ln(x)+1)
What is the first derivative of (2x^{6x}) ?
The first derivative of (2x^{6x}) is 3ln(2)*2^{6x+1}x^{6x}+3*2^{1+6x}x^{6x}(ln(x)+1)