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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}

Popular Examples

integral of 1/10 x

\int \frac{1}{10} x d x

derivative of e^tcos(3t)derivative of

e^{t} cos (3 t)

(\partial)/(\partial y)(x/(1+y))

\frac{\partial}{\partial y} (\frac{x}{1 + y})

y^{''}-10y^'+2y=0

y^{^{''}} - 10 y^{^{'}} + 2 y = 0

(\partial)/(\partial z)(x/(y+z))

\frac{\partial}{\partial z} (\frac{x}{y + z})

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