en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=x^2sqrt(8+x)

Solution

derivative of

y = x^{2} 8 + x

Solution

\frac{5 x ^{2} + 32 x}{2 8 + x}

Solution steps

\frac{d}{d x} (x^{2} 8 + x)

Apply the Product Rule:

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

f = x^{2}, g = 8 + x

= \frac{d}{d x} (x^{2}) 8 + x + \frac{d}{d x} (8 + x) x^{2}

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

\frac{d}{d x} (8 + x) = \frac{1}{2 8 + x}

= 2 x 8 + x + \frac{1}{2 8 + x} x^{2}

Simplify

2 x 8 + x + \frac{1}{2 8 + x} x^{2} : \frac{5 x ^{2} + 32 x}{2 8 + x}

= \frac{5 x ^{2} + 32 x}{2 8 + x}

Popular Examples

sum from n=1 to infinity of ln(1/(n+1))

n = 1 \sum \infty ln (\frac{1}{n + 1})

integral of cosh(x/(27.2632))

\int cosh (\frac{x}{27.2632}) d x

derivative of f(x)=x^3(x^2-4)derivative of

f (x) = x^{3} (x^{2} - 4)

derivative of (x^4e^x/(4^x+3))

\frac{d}{d x} (\frac{x ^{4} e ^{x}}{4 ^{x} + 3})

integral of cos(x)sqrt(1+cos^2(x))

\int cos (x) 1 + cos^{2} (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of y=x^2sqrt(8+x) ?
The derivative of y=x^2sqrt(8+x) is (5x^2+32x)/(2sqrt(8+x))
What is the first derivative of y=x^2sqrt(8+x) ?
The first derivative of y=x^2sqrt(8+x) is (5x^2+32x)/(2sqrt(8+x))