What is the derivative of ln|4+t-t^3| ?

The derivative of ln|4+t-t^3| is (-3t^2+1)/(4+t-t^3)

What is the first derivative of ln|4+t-t^3| ?

The first derivative of ln|4+t-t^3| is (-3t^2+1)/(4+t-t^3)

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derivative of

ln 4 + t - t^{3}

\frac{- 3 t ^{2} + 1}{4 + t - t ^{3}}

Solution steps

\frac{d}{d t} (ln 4 + t - t^{3})

Apply the chain rule:

\frac{1}{∣ 4 + t - t ^{3} ∣} \frac{d}{d t} (4 + t - t^{3})

= \frac{1}{∣ 4 + t - t ^{3} ∣} \frac{d}{d t} (4 + t - t^{3})

\frac{d}{d t} (4 + t - t^{3}) = \frac{( 4 + t - t ^{3} ) ( - 3 t ^{2} + 1 )}{∣ 4 + t - t ^{3} ∣}

= \frac{1}{∣ 4 + t - t ^{3} ∣} \cdot \frac{( 4 + t - t ^{3} ) ( - 3 t ^{2} + 1 )}{∣ 4 + t - t ^{3} ∣}

Simplify

\frac{1}{∣ 4 + t - t ^{3} ∣} \cdot \frac{( 4 + t - t ^{3} ) ( - 3 t ^{2} + 1 )}{∣ 4 + t - t ^{3} ∣} : \frac{- 3 t ^{2} + 1}{4 + t - t ^{3}}

= \frac{- 3 t ^{2} + 1}{4 + t - t ^{3}}

\frac{\partial}{\partial x} (x^{3} - 3 x + y^{3} - 3 y)

\int \frac{3 x + 7}{x ^{2} + 5 x + 6} d x

\int (3 x - 8)^{21} d x

n = 4 \sum \infty \frac{3 ^{n}}{1 0 ^{n}}

What is the derivative of ln|4+t-t^3| ?
The derivative of ln|4+t-t^3| is (-3t^2+1)/(4+t-t^3)
What is the first derivative of ln|4+t-t^3| ?
The first derivative of ln|4+t-t^3| is (-3t^2+1)/(4+t-t^3)