What is the derivative of (4x)^{6x} ?

The derivative of (4x)^{6x} is 3ln(2)*2^{12x+2}x^{6x}+3*2^{1+12x}x^{6x}(ln(x)+1)

What is the first derivative of (4x)^{6x} ?

The first derivative of (4x)^{6x} is 3ln(2)*2^{12x+2}x^{6x}+3*2^{1+12x}x^{6x}(ln(x)+1)

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derivative of

(4 x)^{6 x}

3 ln (2) \cdot 2^{12 x + 2} x^{6 x} + 3 \cdot 2^{1 + 12 x} x^{6 x} (ln (x) + 1)

Solution steps

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

Simplify

(4 x)^{6 x} : 409 6^{x} x^{6 x}

= \frac{d}{d x} (409 6^{x} x^{6 x})

Apply the Product Rule:

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

f = 409 6^{x}, g = x^{6 x}

= \frac{d}{d x} (409 6^{x}) x^{6 x} + \frac{d}{d x} (x^{6 x}) 409 6^{x}

\frac{d}{d x} (409 6^{x}) = 3 ln (2) \cdot 2^{12 x + 2}

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

= 3 ln (2) \cdot 2^{12 x + 2} x^{6 x} + 6 x^{6 x} (ln (x) + 1) \cdot 409 6^{x}

6 x^{6 x} (ln (x) + 1) \cdot 409 6^{x} = 3 \cdot 2^{1 + 12 x} x^{6 x} (ln (x) + 1)

= 3 ln (2) \cdot 2^{12 x + 2} x^{6 x} + 3 \cdot 2^{1 + 12 x} x^{6 x} (ln (x) + 1)

\frac{\partial}{\partial x} (e^{- y} cos (x))

\int \frac{1}{x + x + 1} d x

\frac{d y}{d t} = e^{- 3 t}

cos^{x} (x)

\frac{d ^{2}}{d x ^{2}} (\frac{2 x}{x ^{2} + 1})

What is the derivative of (4x)^{6x} ?
The derivative of (4x)^{6x} is 3ln(2)*2^{12x+2}x^{6x}+3*2^{1+12x}x^{6x}(ln(x)+1)
What is the first derivative of (4x)^{6x} ?
The first derivative of (4x)^{6x} is 3ln(2)*2^{12x+2}x^{6x}+3*2^{1+12x}x^{6x}(ln(x)+1)