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Popular >

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

Solution

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

Solution

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}

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Frequently Asked Questions (FAQ)

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