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Chapter 2: Q. 57 (page 198)

Use the differentiation rules developed in this section to find the derivatives of the functions in Exercises 35-64. Note that it may be necessary to do some preliminary algebra before differentiating.

f(x)=1x3+1x3

Short Answer

Expert verified

The derivative of the function is-3x-52.

Step by step solution

01

Step 1. Given Information

The given function isf(x)=1x3+1x3.

02

Step 2. Simplify

Simplify the given function.

f(x)=1x32+1x32=2x32=2x-32

03

Step 3. Find the derivative

  • Apply the constant multiple of the derivative, (kf)'(x)=kf'(x).

f'(x)=2ddxx-32

  • Apply the power rule of derivative.

f'(x)=2-32x-32-1=-3x-52

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Most popular questions from this chapter

use the definition of derivative to directly prove the differentiation rules for constant and identity function

Prove that if f is a quadratic polynomial function f(x)=ax2+bx+cthen the coefficient of f are completely determined by the values of f(x) and its derivatives at x=0 as follows

a=f"(0)2;b=f'(0);c=f(0)

Use (a) the h鈫�0definition of the derivative and then

(b) the z鈫�cdefinition of the derivative to find f'(c) for each function f and value x=c in Exercises 23鈥�38.

28.f(x)=x4+1,x=2

Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra

f'(x)=7x2+8x11-18;f(0)=-2

Prove, in two ways, that the power rule holds for negative integer powers

a) by using the z鈫�xdefinition of the derivative

b) by using theh鈫�0definition of the derivative
See all solutions

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