Question: "Derivatives Find and simplify the derivative of the..." - Plainmath

Alan Smith

Answered question

2021-12-09

Derivatives Find and simplify the derivative of the following functions.

f (x) = 3 x^{4} (2 x^{2} - 1)

Answer & Explanation

Esta Hurtado

Beginner2021-12-10Added 39 answers

Step 1
To find the derivative of

f (x) = 3 x^{4} (2 x^{2} - 1)

Solution:

f (x) = 3 x^{4} (2 x^{2} - 1)

On simplifying further we get:

f (x) = 3 x^{4} (2 x^{2} - 1)

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

differentiating both sides w.r.t x we get:

f^{'} (x) = \frac{d}{d x} (6 x^{6} - 3 x^{4})

= \frac{d}{d x} (6 x^{6}) - \frac{d}{d x} (3 x^{4})

= 6 (6 x^{5}) - 3 (4 x^{3})

(using,

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

)

= 36 x^{5} - 12 x^{3}

= 12 x^{3} (3 x^{2} - 1)

Step 2
Result:

f^{'} (x) = 12 x^{3} (3 x^{2} - 1)

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