What is the derivative of ln((2x^{3x})) ?

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

What is the first derivative of ln((2x^{3x})) ?

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

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\frac{d}{d x} (ln ((2 x)^{3 x}))

3 (ln (2 x) + 1)

Solution steps

\frac{d}{d x} (ln ((2 x)^{3 x}))

Simplify

ln ((2 x)^{3 x}) : ln (8^{x} x^{3 x})

= \frac{d}{d x} (ln (8^{x} x^{3 x}))

Apply the chain rule:

\frac{1}{8 ^{x} x ^{3 x}} \frac{d}{d x} (8^{x} x^{3 x})

= \frac{1}{8 ^{x} x ^{3 x}} \frac{d}{d x} (8^{x} x^{3 x})

\frac{d}{d x} (8^{x} x^{3 x}) = 3 ln (2) \cdot 8^{x} x^{3 x} + 3 x^{3 x} (ln (x) + 1) \cdot 8^{x}

= \frac{1}{8 ^{x} x ^{3 x}} (3 ln (2) \cdot 8^{x} x^{3 x} + 3 x^{3 x} (ln (x) + 1) \cdot 8^{x})

Simplify

\frac{1}{8 ^{x} x ^{3 x}} (3 ln (2) \cdot 8^{x} x^{3 x} + 3 x^{3 x} (ln (x) + 1) \cdot 8^{x}) : 3 (ln (2 x) + 1)

= 3 (ln (2 x) + 1)

y = x^{2} - 3 x, (3, 0)

t (t - 4) y^{^{'}} + y = 0

x \to 2 lim (9 x^{2})

\frac{s}{( s + 2 ) ^{2}}

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

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