en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x^5-9sqrt(x))

Solution

\frac{d}{d x} ((x^{5} - 9) x)

Solution

\frac{11 x ^{5} - 9}{2 x}

Solution steps

\frac{d}{d x} ((x^{5} - 9) x)

Apply the Product Rule:

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

f = x^{5} - 9, g = x

= \frac{d}{d x} (x^{5} - 9) x + \frac{d}{d x} (x) (x^{5} - 9)

\frac{d}{d x} (x^{5} - 9) = 5 x^{4}

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

= 5 x^{4} x + \frac{1}{2 x} (x^{5} - 9)

Simplify

5 x^{4} x + \frac{1}{2 x} (x^{5} - 9) : \frac{11 x ^{5} - 9}{2 x}

= \frac{11 x ^{5} - 9}{2 x}

Popular Examples

area x=-3,x=1,y=x^3+1,y=0 area

x = - 3, x = 1, y = x^{3} + 1, y = 0

integral from 2 to infinity of xe^{-2x}

\int_{2}^{\infty} x e^{- 2 x} d x

(\partial)/(\partial x)(yx-y-x)

\frac{\partial}{\partial x} (y x - y - x)

derivative of ((1+tan(x)^2)/(sec(x)))

\frac{d}{d x} (\frac{( 1 + tan ( x ) ) ^{2}}{sec ( x )})

(ln (\frac{x}{2}))^{^{'}}

Frequently Asked Questions (FAQ)

What is the derivative of (x^5-9sqrt(x)) ?
The derivative of (x^5-9sqrt(x)) is (11x^5-9)/(2sqrt(x))
What is the first derivative of (x^5-9sqrt(x)) ?
The first derivative of (x^5-9sqrt(x)) is (11x^5-9)/(2sqrt(x))