en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

24 x^{3} + 15 x^{2} - 12

Solution steps

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

Apply the Product Rule:

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

f = 6 x + 5, g = x^{3} - 2

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

\frac{d}{d x} (6 x + 5) = 6

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

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

Simplify

6 (x^{3} - 2) + 3 x^{2} (6 x + 5) : 24 x^{3} + 15 x^{2} - 12

= 24 x^{3} + 15 x^{2} - 12

Popular Examples

integral of (tan(x)+1)/(tan(x)-1)

\int \frac{tan ( x ) + 1}{tan ( x ) - 1} d x

(dy)/(dx)y=(9x-6)/(54x^2)

\frac{d y}{d x} y = \frac{9 x - 6}{54 x ^{2}}

integral of-(e^{2t})/2

\int - \frac{e ^{2 t}}{2} d t

integral from-1 to 2 of (2x^2-4x+5)

\int_{- 1}^{2} (2 x^{2} - 4 x + 5) d x

(\partial)/(\partial x)(2x^4y-2)

\frac{\partial}{\partial x} (2 x^{4} y - 2)

Frequently Asked Questions (FAQ)

What is the derivative of (6x+5(x^3-2)) ?
The derivative of (6x+5(x^3-2)) is 24x^3+15x^2-12
What is the first derivative of (6x+5(x^3-2)) ?
The first derivative of (6x+5(x^3-2)) is 24x^3+15x^2-12