en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^2sqrt(x-5)

Solution

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

Solution

\frac{5 x ^{2} - 20 x}{2 x - 5}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 2 x x - 5 + \frac{1}{2 x - 5} x^{2}

Simplify

2 x x - 5 + \frac{1}{2 x - 5} x^{2} : \frac{5 x ^{2} - 20 x}{2 x - 5}

= \frac{5 x ^{2} - 20 x}{2 x - 5}

Popular Examples

(e^{x + 2})^{^{'}}

d/(d{z)}({x}^{{y}^{{z}}})

\frac{d}{d z} (x^{y^{z}})

sum from n=0 to infinity of 1-(0.2)^n

n = 0 \sum \infty 1 - (0.2)^{n}

derivative of e^{-6x}sin(6x)

\frac{d}{d x} (e^{- 6 x} sin (6 x))

integral of y/(sqrt(1-4y^4))

\int \frac{y}{1 - 4 y ^{4}} d y

Frequently Asked Questions (FAQ)

What is the derivative of x^2sqrt(x-5) ?
The derivative of x^2sqrt(x-5) is (5x^2-20x)/(2sqrt(x-5))
What is the first derivative of x^2sqrt(x-5) ?
The first derivative of x^2sqrt(x-5) is (5x^2-20x)/(2sqrt(x-5))