Q.38 Use the differentiation rules de... [FREE SOLUTION]

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Chapter 2: Q.38 (page 198)

Use the differentiation rules developed in this section to find
the derivatives of the functions
$5 x^{3} - 2 x^{2} + 7$

Short Answer

Expert verified

The derivative of the given function is $15 x^{2} - 4 x$

Step by step solution

Step1. Given information

Given function is $f (x) = 5 x^{3} - 2 x^{2} + 7$

We need to find out the derivatives of the given function.

Step2. finding the derivatives of the function

Here the function is $f (x) = 5 x^{3} - 2 x^{2} + 7$ . When we apply the differentiation rules on the given function , we get

localid="1649266984802" $\frac{d}{d x} (5 x^{3} - 2 x^{2} + 7) = \frac{d (5 x^{3})}{d x} - \frac{d (2 x^{2})}{d x} + \frac{d (7)}{d x} derivative of a constant is 0, thus \frac{d (7)}{d x} = 0 and the derivative of \frac{d}{d x} (x^{n}) = {nx}^{n - 1}, for any non zero rational number n by using power rule hence \frac{d (5 x^{3})}{d x} = 5 \frac{d}{d x} (x^{3}) = 5 脳 3 脳 x^{2} = 15 x^{2} \frac{d (2 x^{2})}{d x} = 2 \frac{d (x^{2})}{d x} = 2 脳 2 x = 4 x thus the derivatives of t he function, \frac{d}{d x} (5 x^{3} - 2 x^{2} + 7) = 15 x^{2} - 4 x + 0 = 15 x^{2} - 4 x$

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91影视

Use the differentiation rules developed in this section to find
the derivatives of the functions
$5 x^{3} - 2 x^{2} + 7$

Short Answer

Step by step solution

Step1. Given information

Step2. finding the derivatives of the function

One App. One Place for Learning.

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91影视

Use the differentiation rules developed in this section to findthe derivatives of the functions5x3-2x2+7

Short Answer

Step by step solution

Step1. Given information

Step2. finding the derivatives of the function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Calculus

Geometry

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Use the differentiation rules developed in this section to find
the derivatives of the functions
$5 x^{3} - 2 x^{2} + 7$