"Find the derivatives f(x)=(x2−2x+1)(x2−1)" was answered by our community

coexpennan

Answered question

2021-03-26

Find the derivatives

f (x) = (x^{2} - 2 x + 1) (x^{2} - 1)

hesgidiauE

Skilled2021-03-28Added 106 answers

Step 1
The given function is

f (x) = (x^{2} - 2 x + 1) (x^{2} - 1)

Step 2
Using formula

\frac{d}{d x} (f . g) = g \frac{d}{d x} f + f \frac{d}{d x} g

\frac{d}{d x} x^{n} = n x^{n - 1}

Step 3
On differentiating

f (x) = (x^{2} - 2 x + 1) (x^{2} - 1)

\frac{d f (x)}{d x} = (x^{2} - 1) \frac{d}{d x} (x^{2} - 2 x + 1) + (x^{2} - 2 x + 1) \frac{d}{d x} (x^{2} - 1)

f^{'} (x) = (x^{2} - 1) (2 x - 2) + (x^{2} - 2 x + 1) (2 x)

f^{'} (x) = (2 x^{3} - 2 x^{2} - 2 x + 2) + (2 x^{3} - 4 x^{2} + 2 x)

f^{'} (x) = 4 x^{3} - 6 x^{2} + 2

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