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

\int \frac{m ^{2}}{m + 1} d m

\frac{64 x}{x ^{2} + 64}

\int x^{2} ln (x) d x

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

\frac{d}{d x} (\frac{x + 10}{x - 10})

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