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

The derivative of 1/4 x^4-2x^3+9/2 x^2+1 is x^3-6x^2+9x

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

The first derivative of 1/4 x^4-2x^3+9/2 x^2+1 is x^3-6x^2+9x

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\frac{d}{d x} (\frac{1}{4} x^{4} - 2 x^{3} + \frac{9}{2} x^{2} + 1)

x^{3} - 6 x^{2} + 9 x

Solution steps

\frac{d}{d x} (\frac{1}{4} x^{4} - 2 x^{3} + \frac{9}{2} x^{2} + 1)

Simplify

\frac{1}{4} x^{4} - 2 x^{3} + \frac{9}{2} x^{2} + 1 : \frac{x ^{4}}{4} - 2 x^{3} + \frac{9 x ^{2}}{2} + 1

= \frac{d}{d x} (\frac{x ^{4}}{4} - 2 x^{3} + \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} (2 x^{3}) + \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} (2 x^{3}) = 6 x^{2}

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

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

= x^{3} - 6 x^{2} + 9 x + 0

Simplify

= x^{3} - 6 x^{2} + 9 x

\int_{0}^{3} \frac{1}{x ^{2} + 3} d x

1 - x - x^{2}

\int tan^{3} (x) sec^{9} (x) d x

\int x^{2} (x + 1)^{3} d x

(3 y^{2} + 2 x y) - (2 x y + x^{2}) \frac{d y}{d x} = 0

What is the derivative of 1/4 x^4-2x^3+9/2 x^2+1 ?
The derivative of 1/4 x^4-2x^3+9/2 x^2+1 is x^3-6x^2+9x
What is the first derivative of 1/4 x^4-2x^3+9/2 x^2+1 ?
The first derivative of 1/4 x^4-2x^3+9/2 x^2+1 is x^3-6x^2+9x