What is the derivative of x^3(8x^2+2x-3^2) ?

The derivative of x^3(8x^2+2x-3^2) is 448x^6+192x^5-220x^4-48x^3+27x^2

What is the first derivative of x^3(8x^2+2x-3^2) ?

The first derivative of x^3(8x^2+2x-3^2) is 448x^6+192x^5-220x^4-48x^3+27x^2

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\frac{d}{d x} (x^{3} (8 x^{2} + 2 x - 3)^{2})

448 x^{6} + 192 x^{5} - 220 x^{4} - 48 x^{3} + 27 x^{2}

Solution steps

\frac{d}{d x} (x^{3} (8 x^{2} + 2 x - 3)^{2})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = (8 x^{2} + 2 x - 3)^{2}

= \frac{d}{d x} (x^{3}) (8 x^{2} + 2 x - 3)^{2} + \frac{d}{d x} ((8 x^{2} + 2 x - 3)^{2}) x^{3}

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

\frac{d}{d x} ((8 x^{2} + 2 x - 3)^{2}) = 2 (8 x^{2} + 2 x - 3) (16 x + 2)

= 3 x^{2} (8 x^{2} + 2 x - 3)^{2} + 2 (8 x^{2} + 2 x - 3) (16 x + 2) x^{3}

Simplify

3 x^{2} (8 x^{2} + 2 x - 3)^{2} + 2 (8 x^{2} + 2 x - 3) (16 x + 2) x^{3} : 448 x^{6} + 192 x^{5} - 220 x^{4} - 48 x^{3} + 27 x^{2}

= 448 x^{6} + 192 x^{5} - 220 x^{4} - 48 x^{3} + 27 x^{2}

x \to + 0 lim (\frac{2 x + 1}{x ^{3}})

\frac{\partial}{\partial y} (x y e^{- 3 y})

x^{2} - 3 x, 5 x, [0, 8]

x^{2} - 1, 0, 2

\int_{0}^{4} 3 t - 8 d t

What is the derivative of x^3(8x^2+2x-3^2) ?
The derivative of x^3(8x^2+2x-3^2) is 448x^6+192x^5-220x^4-48x^3+27x^2
What is the first derivative of x^3(8x^2+2x-3^2) ?
The first derivative of x^3(8x^2+2x-3^2) is 448x^6+192x^5-220x^4-48x^3+27x^2