What is the derivative of sqrt(1+x^3) ?

The derivative of sqrt(1+x^3) is (3x^2)/(2sqrt(1+x^3))

What is the first derivative of sqrt(1+x^3) ?

The first derivative of sqrt(1+x^3) is (3x^2)/(2sqrt(1+x^3))

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derivative of

1 + x^{3}

\frac{3 x ^{2}}{2 1 + x ^{3}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{3 x ^{2}}{2 1 + x ^{3}}

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