High School Mathematics Extensions/Supplementary/Differentiation/Solutions

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Differentiate from first principle

1. (We know that if then )

2.

3.

4.

5. if

f(x)=g(x)+h(x)

then

Differentiating f(z) = (1 - z)^n

1.

2.

3.

4.

Differentiation technique

1.

We use the result of the differentation of f(z)=(1-z)^n (f'(z) = -n(1-z)n-1)

2.

3.

We use the result of exercise 3 of the previous section f(z)= (1+z)3 -> f'(z)=3(1+z)^2

4.

We use the result of the differentation of f(z)=(1-z)^n (f'(z) = -n(1-z)n-1)