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Popular >

derivative of sqrt(t^3-t)

Solution

derivative of

t^{3} - t

Solution

\frac{3 t ^{2} - 1}{2 t ^{3} - t}

Solution steps

\frac{d}{d t} (t^{3} - t)

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 t ^{3} - t} (3 t^{2} - 1) : \frac{3 t ^{2} - 1}{2 t ^{3} - t}

= \frac{3 t ^{2} - 1}{2 t ^{3} - t}

Popular Examples

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\int \frac{13}{x ^{3} - 125} d x

Frequently Asked Questions (FAQ)

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