What is the derivative of f(x)=-1/4 x^4+27/2 x^2 ?

The derivative of f(x)=-1/4 x^4+27/2 x^2 is -x^3+27x

What is the first derivative of f(x)=-1/4 x^4+27/2 x^2 ?

The first derivative of f(x)=-1/4 x^4+27/2 x^2 is -x^3+27x

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derivative of

f (x) = - \frac{1}{4} x^{4} + \frac{27}{2} x^{2}

- x^{3} + 27 x

Solution steps

\frac{d}{d x} (- \frac{1}{4} x^{4} + \frac{27}{2} x^{2})

Simplify

- \frac{1}{4} x^{4} + \frac{27}{2} x^{2} : - \frac{x ^{4}}{4} + \frac{27 x ^{2}}{2}

= \frac{d}{d x} (- \frac{x ^{4}}{4} + \frac{27 x ^{2}}{2})

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (\frac{x ^{4}}{4}) + \frac{d}{d x} (\frac{27 x ^{2}}{2})

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

\frac{d}{d x} (\frac{27 x ^{2}}{2}) = 27 x

= - x^{3} + 27 x

What is the derivative of f(x)=-1/4 x^4+27/2 x^2 ?
The derivative of f(x)=-1/4 x^4+27/2 x^2 is -x^3+27x
What is the first derivative of f(x)=-1/4 x^4+27/2 x^2 ?
The first derivative of f(x)=-1/4 x^4+27/2 x^2 is -x^3+27x