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

The derivative of (3x^4-x^3(x^2+x^3)) is 21x^6+12x^5-5x^4

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

The first derivative of (3x^4-x^3(x^2+x^3)) is 21x^6+12x^5-5x^4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

21 x^{6} + 12 x^{5} - 5 x^{4}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (3 x^{4} - x^{3}) = 12 x^{3} - 3 x^{2}

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

= (12 x^{3} - 3 x^{2}) (x^{2} + x^{3}) + (2 x + 3 x^{2}) (3 x^{4} - x^{3})

Simplify

(12 x^{3} - 3 x^{2}) (x^{2} + x^{3}) + (2 x + 3 x^{2}) (3 x^{4} - x^{3}) : 21 x^{6} + 12 x^{5} - 5 x^{4}

= 21 x^{6} + 12 x^{5} - 5 x^{4}

\frac{\partial}{\partial x} (x y^{3} + 6)

x^{2} y^{^{'}} + y = 0, y (8) = 5

\int_{0}^{3} \frac{1}{( x + 2 ) ( x + 4 )} d x

\frac{10 s}{s ^{2} - 25}

x \to - 5 lim (- 1 x)

What is the derivative of (3x^4-x^3(x^2+x^3)) ?
The derivative of (3x^4-x^3(x^2+x^3)) is 21x^6+12x^5-5x^4
What is the first derivative of (3x^4-x^3(x^2+x^3)) ?
The first derivative of (3x^4-x^3(x^2+x^3)) is 21x^6+12x^5-5x^4