What is the derivative of ln(4x^6+2x^3) ?

The derivative of ln(4x^6+2x^3) is (3(4x^3+1))/(x(2x^3+1))

What is the first derivative of ln(4x^6+2x^3) ?

The first derivative of ln(4x^6+2x^3) is (3(4x^3+1))/(x(2x^3+1))

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\frac{d}{d x} (ln (4 x^{6} + 2 x^{3}))

\frac{3 ( 4 x ^{3} + 1 )}{x ( 2 x ^{3} + 1 )}

Solution steps

\frac{d}{d x} (ln (4 x^{6} + 2 x^{3}))

Apply the chain rule:

\frac{1}{4 x ^{6} + 2 x ^{3}} \frac{d}{d x} (4 x^{6} + 2 x^{3})

= \frac{1}{4 x ^{6} + 2 x ^{3}} \frac{d}{d x} (4 x^{6} + 2 x^{3})

\frac{d}{d x} (4 x^{6} + 2 x^{3}) = 24 x^{5} + 6 x^{2}

= \frac{1}{4 x ^{6} + 2 x ^{3}} (24 x^{5} + 6 x^{2})

Simplify

\frac{1}{4 x ^{6} + 2 x ^{3}} (24 x^{5} + 6 x^{2}) : \frac{3 ( 4 x ^{3} + 1 )}{x ( 2 x ^{3} + 1 )}

= \frac{3 ( 4 x ^{3} + 1 )}{x ( 2 x ^{3} + 1 )}

n = 0 \sum \infty n \cdot 2^{- n}

\int cosh (9 x) d x

\int_{2}^{4} \frac{1}{x ^{2} - 1} d x

\int (4 x - 3)^{3} d x

5 + 4 x^{2} - 2 x^{3}

What is the derivative of ln(4x^6+2x^3) ?
The derivative of ln(4x^6+2x^3) is (3(4x^3+1))/(x(2x^3+1))
What is the first derivative of ln(4x^6+2x^3) ?
The first derivative of ln(4x^6+2x^3) is (3(4x^3+1))/(x(2x^3+1))