What is the derivative of y=3x(6x-5x^2) ?

The derivative of y=3x(6x-5x^2) is 3(-15x^2+12x)

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

The first derivative of y=3x(6x-5x^2) is 3(-15x^2+12x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = 3 x (6 x - 5 x^{2})

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)

y^{^{''}} - y^{^{'}} - 12 y = 0

\int \frac{x}{x ^{2} + x + 1} d x

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

\int_{1}^{2} \frac{1}{t} d t

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

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