What is the derivative of sqrt(x^5+3) ?

The derivative of sqrt(x^5+3) is (5x^4)/(2sqrt(x^5+3))

What is the first derivative of sqrt(x^5+3) ?

The first derivative of sqrt(x^5+3) is (5x^4)/(2sqrt(x^5+3))

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\frac{d}{d x} (x^{5} + 3)

\frac{5 x ^{4}}{2 x ^{5} + 3}

Solution steps

\frac{d}{d x} (x^{5} + 3)

Apply the chain rule:

\frac{1}{2 x ^{5} + 3} \frac{d}{d x} (x^{5} + 3)

= \frac{1}{2 x ^{5} + 3} \frac{d}{d x} (x^{5} + 3)

\frac{d}{d x} (x^{5} + 3) = 5 x^{4}

= \frac{1}{2 x ^{5} + 3} \cdot 5 x^{4}

Simplify

\frac{1}{2 x ^{5} + 3} \cdot 5 x^{4} : \frac{5 x ^{4}}{2 x ^{5} + 3}

= \frac{5 x ^{4}}{2 x ^{5} + 3}

What is the derivative of sqrt(x^5+3) ?
The derivative of sqrt(x^5+3) is (5x^4)/(2sqrt(x^5+3))
What is the first derivative of sqrt(x^5+3) ?
The first derivative of sqrt(x^5+3) is (5x^4)/(2sqrt(x^5+3))