What is the derivative of sqrt(x^3+10) ?

The derivative of sqrt(x^3+10) is (3x^2)/(2sqrt(x^3+10))

What is the first derivative of sqrt(x^3+10) ?

The first derivative of sqrt(x^3+10) is (3x^2)/(2sqrt(x^3+10))

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\frac{d}{d x} (x^{3} + 10)

\frac{3 x ^{2}}{2 x ^{3} + 10}

Solution steps

\frac{d}{d x} (x^{3} + 10)

Apply the chain rule:

\frac{1}{2 x ^{3} + 10} \frac{d}{d x} (x^{3} + 10)

= \frac{1}{2 x ^{3} + 10} \frac{d}{d x} (x^{3} + 10)

\frac{d}{d x} (x^{3} + 10) = 3 x^{2}

= \frac{1}{2 x ^{3} + 10} \cdot 3 x^{2}

Simplify

\frac{1}{2 x ^{3} + 10} \cdot 3 x^{2} : \frac{3 x ^{2}}{2 x ^{3} + 10}

= \frac{3 x ^{2}}{2 x ^{3} + 10}

What is the derivative of sqrt(x^3+10) ?
The derivative of sqrt(x^3+10) is (3x^2)/(2sqrt(x^3+10))
What is the first derivative of sqrt(x^3+10) ?
The first derivative of sqrt(x^3+10) is (3x^2)/(2sqrt(x^3+10))