What is the derivative of 3x^4+1/(3x^4+3/(2x^2)) ?

The derivative of 3x^4+1/(3x^4+3/(2x^2)) is 12x^3-4/(3x^5)-3/(x^3)

What is the first derivative of 3x^4+1/(3x^4+3/(2x^2)) ?

The first derivative of 3x^4+1/(3x^4+3/(2x^2)) is 12x^3-4/(3x^5)-3/(x^3)

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\frac{d}{d x} (3 x^{4} + \frac{1}{3 x ^{4}} + \frac{3}{2 x ^{2}})

12 x^{3} - \frac{4}{3 x ^{5}} - \frac{3}{x ^{3}}

Solution steps

\frac{d}{d x} (3 x^{4} + \frac{1}{3 x ^{4}} + \frac{3}{2 x ^{2}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3 x^{4}) + \frac{d}{d x} (\frac{1}{3 x ^{4}}) + \frac{d}{d x} (\frac{3}{2 x ^{2}})

\frac{d}{d x} (3 x^{4}) = 12 x^{3}

\frac{d}{d x} (\frac{1}{3 x ^{4}}) = - \frac{4}{3 x ^{5}}

\frac{d}{d x} (\frac{3}{2 x ^{2}}) = - \frac{3}{x ^{3}}

= 12 x^{3} - \frac{4}{3 x ^{5}} - \frac{3}{x ^{3}}

What is the derivative of 3x^4+1/(3x^4+3/(2x^2)) ?
The derivative of 3x^4+1/(3x^4+3/(2x^2)) is 12x^3-4/(3x^5)-3/(x^3)
What is the first derivative of 3x^4+1/(3x^4+3/(2x^2)) ?
The first derivative of 3x^4+1/(3x^4+3/(2x^2)) is 12x^3-4/(3x^5)-3/(x^3)