   Chapter 3.1, Problem 28E

Chapter
Section
Textbook Problem

Differentiate the function. F ( z ) = A + B z + C z 2 z 2

To determine

To find: The derivative of the function F(z)=A+Bz+Cz2z2.

Explanation

Given:

The function, F(z)=A+Bz+Cz2z2.

Formula used:

Derivative of a Constant Function:

If c is a constant function, then ddz(c)=0. (1)

The Constant Multiple Rule:

If c is a constant and f(z) is a differentiable function, then the constant multiple rule is,

ddz[cf(z)]=cddzf(z) (2)

The Power Rule:

If n is any real number, then the power rule is,

ddz(zn)=nzn1 (3)

The Sum Rule:

If f(z) and g(z) are both differentiable functions, then the sum rule is,

ddz[f(z)+g(z)]=ddz(f(z))+ddz(g(z)) (4)

Calculation:

The derivative of F(z) is F(z) is as follows:

F(z)=ddz(F(z)) =ddz(A+Bz+Cz2z2)=ddz(Az2+Bzz2+Cz2z2)=ddz(Az2+Bz+C)

F(z)=ddz(Az2+Bz1+C)

Apply the sum rule as shown in equation (4)

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