What is the derivative of ln(x^4+27) ?

The derivative of ln(x^4+27) is (4x^3)/(x^4+27)

What is the first derivative of ln(x^4+27) ?

The first derivative of ln(x^4+27) is (4x^3)/(x^4+27)

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\frac{d}{d x} (ln (x^{4} + 27))

\frac{4 x ^{3}}{x ^{4} + 27}

Solution steps

\frac{d}{d x} (ln (x^{4} + 27))

Apply the chain rule:

\frac{1}{x ^{4} + 27} \frac{d}{d x} (x^{4} + 27)

= \frac{1}{x ^{4} + 27} \frac{d}{d x} (x^{4} + 27)

\frac{d}{d x} (x^{4} + 27) = 4 x^{3}

= \frac{1}{x ^{4} + 27} \cdot 4 x^{3}

Simplify

\frac{1}{x ^{4} + 27} \cdot 4 x^{3} : \frac{4 x ^{3}}{x ^{4} + 27}

= \frac{4 x ^{3}}{x ^{4} + 27}

\int \frac{1}{9 x ^{3}} d x

\int_{1.5}^{2} \frac{2 x}{3} d x

4 y^{^{''}} + 10 y = 0

x \to 2 - lim (x - 2)

\int 28 x (7 x^{2} - 5)^{3} d x

What is the derivative of ln(x^4+27) ?
The derivative of ln(x^4+27) is (4x^3)/(x^4+27)
What is the first derivative of ln(x^4+27) ?
The first derivative of ln(x^4+27) is (4x^3)/(x^4+27)