What is the derivative of f(x)=5x^4+1/(2x^2) ?

The derivative of f(x)=5x^4+1/(2x^2) is 20x^3-1/(x^3)

What is the first derivative of f(x)=5x^4+1/(2x^2) ?

The first derivative of f(x)=5x^4+1/(2x^2) is 20x^3-1/(x^3)

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derivative of

f (x) = 5 x^{4} + \frac{1}{2 x ^{2}}

20 x^{3} - \frac{1}{x ^{3}}

Solution steps

\frac{d}{d x} (5 x^{4} + \frac{1}{2 x ^{2}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5 x^{4}) + \frac{d}{d x} (\frac{1}{2 x ^{2}})

\frac{d}{d x} (5 x^{4}) = 20 x^{3}

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

= 20 x^{3} - \frac{1}{x ^{3}}

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What is the derivative of f(x)=5x^4+1/(2x^2) ?
The derivative of f(x)=5x^4+1/(2x^2) is 20x^3-1/(x^3)
What is the first derivative of f(x)=5x^4+1/(2x^2) ?
The first derivative of f(x)=5x^4+1/(2x^2) is 20x^3-1/(x^3)