en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (2x^3-3(sin(x)+2))

Solution

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

Solution

6 x^{2} (sin (x) + 2) + cos (x) (2 x^{3} - 3)

Solution steps

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

Apply the Product Rule:

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

f = 2 x^{3} - 3, g = sin (x) + 2

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

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

\frac{d}{d x} (sin (x) + 2) = cos (x)

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

Popular Examples

area 3cos(x),3cos(2x),0<= x<= pi area

3 cos (x), 3 cos (2 x), 0 \leq x \leq π

(1+y^2sin(2x))dx-2ycos^2(x)dy=0

(1 + y^{2} sin (2 x)) d x - 2 y cos^{2} (x) d y = 0

\frac{d y}{d x} = x y^{3}

integral of 1/(x^2+12)

\int \frac{1}{x ^{2} + 12} d x

area 3x,9x^2 area

3 x, 9 x^{2}

Frequently Asked Questions (FAQ)

What is the derivative of (2x^3-3(sin(x)+2)) ?
The derivative of (2x^3-3(sin(x)+2)) is 6x^2(sin(x)+2)+cos(x)(2x^3-3)
What is the first derivative of (2x^3-3(sin(x)+2)) ?
The first derivative of (2x^3-3(sin(x)+2)) is 6x^2(sin(x)+2)+cos(x)(2x^3-3)