Chapter 2: Q. 60 (page 222)

In Exercises 59–63, find a function f that has the given derivative f'. In each case you can find the answer with an educated guess-and-check process.
$f' (x) = x^{2} e^{x^{3}}$

Short Answer

Expert verified

The required function is $f (x) = \frac{1}{3} e^{x^{3}}$

Step by step solution

Step 1. Given Information

The given derivative is $f' (x) = x^{2} e^{x^{3}}$

Step 2. Calculation

We will use a targeted guess and check method to find an antiderivative of given derivative.

$\frac{d}{d x} f (x) = \frac{d}{d x} (\frac{1}{3} e^{x^{3}}) = \frac{1}{3} e^{x^{3}} \frac{d}{d x} (x^{3}) = \frac{1}{3} e^{x^{3}} (3 x^{2}) = x^{2} e^{x^{3}}$

Thus, we get the required function.

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In Exercises 59–63, find a function f that has the given derivative f'. In each case you can find the answer with an educated guess-and-check process.
$f' (x) = x^{2} e^{x^{3}}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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In Exercises 59–63, find a function f that has the given derivative f'. In each case you can find the answer with an educated guess-and-check process.f'(x)=x2ex3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Pure Maths

Geometry

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Exercises 59–63, find a function f that has the given derivative f'. In each case you can find the answer with an educated guess-and-check process.
$f' (x) = x^{2} e^{x^{3}}$