What is the derivative of f(x)=4x^4-1/(4x^4) ?

The derivative of f(x)=4x^4-1/(4x^4) is 16x^3+1/(x^5)

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

The first derivative of f(x)=4x^4-1/(4x^4) is 16x^3+1/(x^5)

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derivative

16 x^{3} + \frac{1}{x ^{5}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (4 x^{4}) = 16 x^{3}

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

= 16 x^{3} - (- \frac{1}{x ^{5}})

Simplify

= 16 x^{3} + \frac{1}{x ^{5}}

What is the derivative of f(x)=4x^4-1/(4x^4) ?
The derivative of f(x)=4x^4-1/(4x^4) is 16x^3+1/(x^5)
What is the first derivative of f(x)=4x^4-1/(4x^4) ?
The first derivative of f(x)=4x^4-1/(4x^4) is 16x^3+1/(x^5)