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Popular >

derivative of 1/(1+x^3)

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

integral of (x^2-x+24)/(x^3+6x)

\int \frac{x ^{2} - x + 24}{x ^{3} + 6 x} d x

tangent of y=x-3x^2,(3,-24)tangent of

y = x - 3 x^{2}, (3, - 24)

derivative of f(t)=e^{8tsin(2t)}derivative of

f (t) = e^{8 t s i n (2 t)}

(\partial)/(\partial x)(3x^2y^4-2)

\frac{\partial}{\partial x} (3 x^{2} y^{4} - 2)

integral of (5x-7)e^{5x-7}

\int (5 x - 7) e^{5 x - 7} d x

Frequently Asked Questions (FAQ)

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