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Popular >

derivative of 1/(x^3+1)

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(dy)/(dx)=xy+4x+5y+20

\frac{d y}{d x} = x y + 4 x + 5 y + 20

integral of ((x-2)(x+2))/(x^2)

\int \frac{( x - 2 ) ( x + 2 )}{x ^{2}} d x

integral from 0 to 2 of 3/(sqrt(16-x^2))

\int_{0}^{2} \frac{3}{16 - x ^{2}} d x

derivative of (cos(x)^{pi/5})

\frac{d}{d x} ((cos (x))^{\frac{π}{5}})

integral from-2 to 3 of (45)/(x^4)

\int_{- 2}^{3} \frac{45}{x ^{4}} d x

Frequently Asked Questions (FAQ)

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