en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (2x-sqrt(x)(5x+2))

Solution

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

Solution

\frac{- 15 x + 40 x x - 2}{2 x} + 4

Solution steps

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

Apply the Product Rule:

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

f = 2 x - x, g = 5 x + 2

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

\frac{d}{d x} (2 x - x) = 2 - \frac{1}{2 x}

\frac{d}{d x} (5 x + 2) = 5

= (2 - \frac{1}{2 x}) (5 x + 2) + 5 (2 x - x)

Simplify

(2 - \frac{1}{2 x}) (5 x + 2) + 5 (2 x - x) : \frac{- 15 x + 40 x x - 2}{2 x} + 4

= \frac{- 15 x + 40 x x - 2}{2 x} + 4

Graph

Popular Examples

integral of (sin^2(x))/(cos^4(x))

\int \frac{sin ^{2} ( x )}{cos ^{4} ( x )} d x

sum from n=0 to infinity of e^{-0.06n}

n = 0 \sum \infty e^{- 0.06 n}

y^{''}-5y^'+6y=2e^{t/2}

y^{^{''}} - 5 y^{^{'}} + 6 y = 2 e^{\frac{t}{2}}

derivative of csc^7(2x^pi+pi^3)

\frac{d}{d x} (csc^{7} (2 x^{π} + π^{3}))

area sin^2(x),sin^4(x),[0,pi]area

sin^{2} (x), sin^{4} (x), [0, π]

Frequently Asked Questions (FAQ)

What is the derivative of (2x-sqrt(x)(5x+2)) ?
The derivative of (2x-sqrt(x)(5x+2)) is (-15x+40xsqrt(x)-2)/(2sqrt(x))+4
What is the first derivative of (2x-sqrt(x)(5x+2)) ?
The first derivative of (2x-sqrt(x)(5x+2)) is (-15x+40xsqrt(x)-2)/(2sqrt(x))+4