What is the derivative of (x^4/4-9/2 x^2+1) ?

The derivative of (x^4/4-9/2 x^2+1) is x^3-9x

What is the first derivative of (x^4/4-9/2 x^2+1) ?

The first derivative of (x^4/4-9/2 x^2+1) is x^3-9x

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\frac{d}{d x} (\frac{x ^{4}}{4} - \frac{9}{2} x^{2} + 1)

x^{3} - 9 x

Solution steps

\frac{d}{d x} (\frac{x ^{4}}{4} - \frac{9}{2} x^{2} + 1)

Simplify

\frac{x ^{4}}{4} - \frac{9}{2} x^{2} + 1 : \frac{x ^{4}}{4} - \frac{9 x ^{2}}{2} + 1

= \frac{d}{d x} (\frac{x ^{4}}{4} - \frac{9 x ^{2}}{2} + 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{4}}{4}) - \frac{d}{d x} (\frac{9 x ^{2}}{2}) + \frac{d}{d x} (1)

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

\frac{d}{d x} (\frac{9 x ^{2}}{2}) = 9 x

\frac{d}{d x} (1) = 0

= x^{3} - 9 x + 0

Simplify

= x^{3} - 9 x

\int (x + y)^{2} d x

x \to 0 lim (\frac{sin ( 4 x )}{tan ( 3 x )})

\int_{1}^{\infty} 12 e^{- 6 x} d x

\frac{10 s ^{2}}{s ^{2} + 9}

x \to 1 lim (x^{2} + 5)

What is the derivative of (x^4/4-9/2 x^2+1) ?
The derivative of (x^4/4-9/2 x^2+1) is x^3-9x
What is the first derivative of (x^4/4-9/2 x^2+1) ?
The first derivative of (x^4/4-9/2 x^2+1) is x^3-9x