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Given h(t)=\sqrt t(1-t^2), find h'(t).

Question:

Given {eq}h(t)=\sqrt t(1-t^2){/eq}, find {eq}h'(t){/eq}.

Differentiation

This question is a differentiation question we have to find out the derivative of the given function. To solve this question, we use the chain rule.

Answer and Explanation:

{eq}\Rightarrow \ h(t)=\sqrt{t}(1-t^{2})\\ \Rightarrow \ h(t)=\sqrt{t}-t^{\frac{5}{2}}\\ \text{differentiate with respect to t}\\ \Rightarrow \ h'(t)=\frac{1}{2\sqrt{t}}-\frac{5}{2}t^{\frac{3}{2}}\\ \Rightarrow \ h'(t)=\frac{1-5t^{2}}{2\sqrt{t}} {/eq}


Learn more about this topic:

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Solving Partial Derivative Equations

from GRE Math: Study Guide & Test Prep

Chapter 14 / Lesson 1
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