How do you find the instantaneous rate of change of w with respect to z for w=1/z+z/2?

1 Answer
Psykolord1989 . · Manish Bhardwaj · Gaurav
Sep 28, 2014

(dw)/dz = -1/z^2 + 1/2

Explanation :

(dw)/dz = d/dz (1/z + z/2)

Initial set-up.

(dw)/dz = d / dz ( 1/z) + d /dz ( z/2)

The derivative of a sum is equal to the sum of the derivatives.

(dw)/dz = d/dz (z^-1) + 1/2 d/dz (z)

First part: A function f(z) = c/(z^n) with c constant can also be written as f(z) = cz^(-n) Second part: d/dz cf(z) = c d/dz f(z) if c is constant.

(dw)/dz = -1*z^ -2 + 1/2*1

Use of the power rule: d/dz z^n = nz^(n-1). Then d/dz z = d/dz z^1 = z^0 = 1

(dw)/dz = -z^ -2 + 1/2

Multiplicative identity postulate.

(dw)/dz = -1/z^2 + 1/2

A function written as f(z) = cz^(-n) can also be written f(z) = c/(z^n)

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