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Popular >

derivative of ln(6-x^2+2x^4)

Solution

derivative of

ln (6 - x^{2} + 2 x^{4})

Solution

\frac{8 x ^{3} - 2 x}{6 - x ^{2} + 2 x ^{4}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (6 - x^{2} + 2 x^{4}) = 8 x^{3} - 2 x

= \frac{1}{6 - x ^{2} + 2 x ^{4}} (8 x^{3} - 2 x)

Simplify

\frac{1}{6 - x ^{2} + 2 x ^{4}} (8 x^{3} - 2 x) : \frac{8 x ^{3} - 2 x}{6 - x ^{2} + 2 x ^{4}}

= \frac{8 x ^{3} - 2 x}{6 - x ^{2} + 2 x ^{4}}

Popular Examples

integral from 1 to infinity of 7/(x^2+1)

\int_{1}^{\infty} \frac{7}{x ^{2} + 1} d x

derivative of y=(((x^2-2)/(2x^2+1))^2)derivative of

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

integral of sqrt(6)

\int 6 d x

derivative of |2x-1|

\frac{d}{d x} (∣ 2 x - 1 ∣)

(\partial)/(\partial x)(((x-y))/(x+y))

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

Frequently Asked Questions (FAQ)

What is the derivative of ln(6-x^2+2x^4) ?
The derivative of ln(6-x^2+2x^4) is (8x^3-2x)/(6-x^2+2x^4)
What is the first derivative of ln(6-x^2+2x^4) ?
The first derivative of ln(6-x^2+2x^4) is (8x^3-2x)/(6-x^2+2x^4)