What is the derivative of-x^3+5ax^2-3a^2x-b ?

The derivative of-x^3+5ax^2-3a^2x-b is -3x^2+10ax-3a^2

What is the first derivative of-x^3+5ax^2-3a^2x-b ?

The first derivative of-x^3+5ax^2-3a^2x-b is -3x^2+10ax-3a^2

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\frac{d}{d x} (- x^{3} + 5 a x^{2} - 3 a^{2} x - b)

- 3 x^{2} + 10 a x - 3 a^{2}

Solution steps

\frac{d}{d x} (- x^{3} + 5 a x^{2} - 3 a^{2} x - b)

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (x^{3}) + \frac{d}{d x} (5 a x^{2}) - \frac{d}{d x} (3 a^{2} x) - \frac{d b}{d x}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (5 a x^{2}) = 10 a x

\frac{d}{d x} (3 a^{2} x) = 3 a^{2}

\frac{d b}{d x} = 0

= - 3 x^{2} + 10 a x - 3 a^{2} - 0

Simplify

= - 3 x^{2} + 10 a x - 3 a^{2}

What is the derivative of-x^3+5ax^2-3a^2x-b ?
The derivative of-x^3+5ax^2-3a^2x-b is -3x^2+10ax-3a^2
What is the first derivative of-x^3+5ax^2-3a^2x-b ?
The first derivative of-x^3+5ax^2-3a^2x-b is -3x^2+10ax-3a^2