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Differentiate the function. h(t) = \sqrt[4]{t} - 4 e^ r

Question:

Differentiate the function.

{eq}h(t) = \sqrt[4]{t} - 4 e^ r {/eq}

Answer and Explanation:

We wish to find the derivative of this function. Since our function is in terms of t, so will our derivative. However, we have a term containing another variable, r. We can't also differentiate with respect to this variable, so we will treat this number as a constant.

Let's start by rewriting the fourth root as an exponent. This will allow us to use the Power Rule easier.

{eq}h(t) = t^{\frac{1}{4}} - 4e^r {/eq}

We can now differentiate term by term with respect to t.

{eq}\begin{align*} h'(t) &= \frac{1}{4}t^{-\frac{3}{4}} - 0\\ &= \frac{1}{4 \sqrt[4]{t^3}} \end{align*} {/eq}

Therefore, the derivative of this function with respect to t is {eq}h'(t) = \frac{1}{4 \sqrt[4]{t^3}} {/eq}.


Learn more about this topic:

Partial Derivative: Definition, Rules & Examples

from College Algebra: Help and Review

Chapter 18 / Lesson 12
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