Best solutions to - "Find the derivatives. f(x)=3x3−42x2+3" - Plainmath

nicekikah

Answered question

2021-02-16

Find the derivatives.

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

Answer & Explanation

estenutC

Skilled2021-02-18Added 81 answers

Use quotient rule of derivative and find the derivatives of above function.

\frac{d}{d x} (\frac{f (x)}{g (x)}) = \frac{f^{'} (x) g (x) - g^{'} (x) f (x)}{{[g (x)]}^{2}}

[Quotient rule]

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

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

= \frac{(2 x^{2} + 3) (9 x^{2}) - (3 x^{3} - 4) (4 x)}{{(2 x^{2} + 3)}^{2}}

= \frac{18 x^{4} + 27 x^{2} - 12 x^{4} + 16 x}{{(2 x^{2} + 3)}^{2}}

= \frac{6 x^{4} + 27 x^{2} + 16 x}{{(2 x^{2} + 3)}^{2}}

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