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

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

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

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

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derivative of

ln (e^{l n (x^{3} + 1)})

\frac{3 x ^{2}}{x ^{3} + 1}

Solution steps

\frac{d}{d x} (ln (e^{l n (x^{3} + 1)}))

Simplify

ln (e^{l n (x^{3} + 1)}) : ln (x^{3} + 1)

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

Apply the chain rule:

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

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

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

= \frac{1}{x ^{3} + 1} \cdot 3 x^{2}

Simplify

\frac{1}{x ^{3} + 1} \cdot 3 x^{2} : \frac{3 x ^{2}}{x ^{3} + 1}

= \frac{3 x ^{2}}{x ^{3} + 1}

y = (6 x - 3) (3 x + 9)

\frac{d}{d t} (100 + 10 t + 1.25 t)

y = \frac{arcsin ( 1 )}{x}

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

\frac{d}{d x} ((x + z) (x - 5)^{8})

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