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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derivative of

(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)

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(cos^{3} (t))^{^{'}}

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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)