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

x \to π lim (x cos (\frac{7 x}{6}))

\frac{x}{x + 6}

\int - \frac{2}{7 - 7 x ^{2}} d x

\frac{d}{d x} (5 x^{3} - 3 x^{5})

t \to - 2 lim ((t + 4)^{2})

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)