What is the derivative of x^4+8x^3+6x^2-40x+25 ?

The derivative of x^4+8x^3+6x^2-40x+25 is 4x^3+24x^2+12x-40

What is the first derivative of x^4+8x^3+6x^2-40x+25 ?

The first derivative of x^4+8x^3+6x^2-40x+25 is 4x^3+24x^2+12x-40

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (x^{4} + 8 x^{3} + 6 x^{2} - 40 x + 25)

4 x^{3} + 24 x^{2} + 12 x - 40

Solution steps

\frac{d}{d x} (x^{4} + 8 x^{3} + 6 x^{2} - 40 x + 25)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{4}) + \frac{d}{d x} (8 x^{3}) + \frac{d}{d x} (6 x^{2}) - \frac{d}{d x} (40 x) + \frac{d}{d x} (25)

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

\frac{d}{d x} (8 x^{3}) = 24 x^{2}

\frac{d}{d x} (6 x^{2}) = 12 x

\frac{d}{d x} (40 x) = 40

\frac{d}{d x} (25) = 0

= 4 x^{3} + 24 x^{2} + 12 x - 40 + 0

Simplify

= 4 x^{3} + 24 x^{2} + 12 x - 40

What is the derivative of x^4+8x^3+6x^2-40x+25 ?
The derivative of x^4+8x^3+6x^2-40x+25 is 4x^3+24x^2+12x-40
What is the first derivative of x^4+8x^3+6x^2-40x+25 ?
The first derivative of x^4+8x^3+6x^2-40x+25 is 4x^3+24x^2+12x-40