Resolved: "Find the derivatives of f(x)=(−3+x−3)(−4x3+3) using product rules."

tinfoQ

Answered question

2021-06-03

Find the derivatives of

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

using product rules.

Leonard Stokes

Skilled2021-06-04Added 98 answers

Step 1
We need to find the derivatives of

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

using product rules.
Step 2
Now differentiating the given function,

\frac{d}{d x} [f (x)] = \frac{d}{d x} [(- 3 + x^{- 3}) (- 4 x^{3} + 3)]

= (- 3 + x^{- 3}) \frac{d}{d x} (- 4 x^{3} + 3) + (- 4 x^{3} + 3) \frac{d}{d x} (- 3 + x^{- 3})

[Using product rule of derivative]

= (- 3 + x^{- 3}) (- 12 x^{2} + 0) + (- 4 x^{3} + 3) (- 0 - 3 x^{- 4})

= 36 x^{2} - 12 x^{- 1} + 12 x^{- 1} - 9 x^{- 4}

= 36 x^{2} - 9 x^{- 4}

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