What is the derivative of x^3(3x^6-5x^2+4) ?

The derivative of x^3(3x^6-5x^2+4) is 27x^8-25x^4+12x^2

What is the first derivative of x^3(3x^6-5x^2+4) ?

The first derivative of x^3(3x^6-5x^2+4) is 27x^8-25x^4+12x^2

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\frac{d}{d x} (x^{3} (3 x^{6} - 5 x^{2} + 4))

27 x^{8} - 25 x^{4} + 12 x^{2}

Solution steps

\frac{d}{d x} (x^{3} (3 x^{6} - 5 x^{2} + 4))

Apply the Product Rule:

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

f = x^{3}, g = 3 x^{6} - 5 x^{2} + 4

= \frac{d}{d x} (x^{3}) (3 x^{6} - 5 x^{2} + 4) + \frac{d}{d x} (3 x^{6} - 5 x^{2} + 4) x^{3}

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

\frac{d}{d x} (3 x^{6} - 5 x^{2} + 4) = 18 x^{5} - 10 x

= 3 x^{2} (3 x^{6} - 5 x^{2} + 4) + (18 x^{5} - 10 x) x^{3}

Simplify

3 x^{2} (3 x^{6} - 5 x^{2} + 4) + (18 x^{5} - 10 x) x^{3} : 27 x^{8} - 25 x^{4} + 12 x^{2}

= 27 x^{8} - 25 x^{4} + 12 x^{2}

y = x, y = x, x = 4

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

cos (x) \frac{d y}{d x} + (sin (x)) y = 1

\frac{\partial}{\partial y} (e^{x^{2} + y^{2}} sin (x y))

\int \frac{5 + 5 x + 5}{x + 5} d x

What is the derivative of x^3(3x^6-5x^2+4) ?
The derivative of x^3(3x^6-5x^2+4) is 27x^8-25x^4+12x^2
What is the first derivative of x^3(3x^6-5x^2+4) ?
The first derivative of x^3(3x^6-5x^2+4) is 27x^8-25x^4+12x^2