en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 3x(6x-5x^2)

Solution

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

Solution

3 (- 15 x^{2} + 12 x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (6 x - 5 x^{2}) = 6 - 10 x

= 3 (1 \cdot (6 x - 5 x^{2}) + (6 - 10 x) x)

Simplify

3 (1 \cdot (6 x - 5 x^{2}) + (6 - 10 x) x) : 3 (- 15 x^{2} + 12 x)

= 3 (- 15 x^{2} + 12 x)

Popular Examples

derivative of (80e^{-x/(10})-40x)

\frac{d}{d x} ((80 e^{- \frac{x}{10}}) - 40 x)

area x^2-2x,3x+6 area

x^{2} - 2 x, 3 x + 6

limit as x approaches 3 of-3

x \to 3 lim (- 3)

derivative of y=((x^2+2)/(x^2-2))^6 derivative of

y = (\frac{x ^{2} + 2}{x ^{2} - 2})^{6}

(\partial)/(\partial x)(xln(z^3+x^6))

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

Frequently Asked Questions (FAQ)

What is the derivative of 3x(6x-5x^2) ?
The derivative of 3x(6x-5x^2) is 3(-15x^2+12x)
What is the first derivative of 3x(6x-5x^2) ?
The first derivative of 3x(6x-5x^2) is 3(-15x^2+12x)