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Popular >

derivative of h(t)=sqrt(t)(1-t^2)

Solution

derivative of

h (t) = t (1 - t^{2})

Solution

\frac{1 - 5 t ^{2}}{2 t}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t, g = 1 - t^{2}

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

\frac{d}{d t} (t) = \frac{1}{2 t}

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

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

Simplify

\frac{1}{2 t} (1 - t^{2}) + (- 2 t) t : \frac{1 - 5 t ^{2}}{2 t}

= \frac{1 - 5 t ^{2}}{2 t}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of h(t)=sqrt(t)(1-t^2) ?
The derivative of h(t)=sqrt(t)(1-t^2) is (1-5t^2)/(2sqrt(t))
What is the first derivative of h(t)=sqrt(t)(1-t^2) ?
The first derivative of h(t)=sqrt(t)(1-t^2) is (1-5t^2)/(2sqrt(t))