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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\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}

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