What is the derivative of (4x^{3x}) ?

The derivative of (4x^{3x}) is 3ln(2)*2^{6x+1}x^{3x}+3x^{3x}(ln(x)+1)*64^x

What is the first derivative of (4x^{3x}) ?

The first derivative of (4x^{3x}) is 3ln(2)*2^{6x+1}x^{3x}+3x^{3x}(ln(x)+1)*64^x

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\frac{d}{d x} ((4 x)^{3 x})

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

Solution steps

\frac{d}{d x} ((4 x)^{3 x})

Simplify

(4 x)^{3 x} : 6 4^{x} x^{3 x}

= \frac{d}{d x} (6 4^{x} x^{3 x})

Apply the Product Rule:

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

f = 6 4^{x}, g = x^{3 x}

= \frac{d}{d x} (6 4^{x}) x^{3 x} + \frac{d}{d x} (x^{3 x}) 6 4^{x}

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

\frac{d}{d x} (x^{3 x}) = 3 x^{3 x} (ln (x) + 1)

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

What is the derivative of (4x^{3x}) ?
The derivative of (4x^{3x}) is 3ln(2)*2^{6x+1}x^{3x}+3x^{3x}(ln(x)+1)*64^x
What is the first derivative of (4x^{3x}) ?
The first derivative of (4x^{3x}) is 3ln(2)*2^{6x+1}x^{3x}+3x^{3x}(ln(x)+1)*64^x