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

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

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

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

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derivative of

y = x^{3} + 1

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

arcsin (\frac{x}{4})

x \to \infty lim (x^{2 x})

\frac{d}{d x} (cos (2 x) + sin (2 π))

\int_{1}^{t} \frac{25}{x ^{3}} d x

\frac{d}{d x} (cos (x + a))

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