What is the derivative of (\sqrt[3]{x}(sqrt(x)+3)) ?

The derivative of (\sqrt[3]{x}(sqrt(x)+3)) is (5sqrt(x)+6)/(6x^{2/3)}

What is the first derivative of (\sqrt[3]{x}(sqrt(x)+3)) ?

The first derivative of (\sqrt[3]{x}(sqrt(x)+3)) is (5sqrt(x)+6)/(6x^{2/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} ((3 x) (x + 3))

\frac{5 x + 6}{6 x ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} ((3 x) (x + 3))

Apply the Product Rule:

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

f = 3 x, g = x + 3

= \frac{d}{d x} (3 x) (x + 3) + \frac{d}{d x} (x + 3) 3 x

\frac{d}{d x} (3 x) = \frac{1}{3 x ^{\frac{2}{3}}}

\frac{d}{d x} (x + 3) = \frac{1}{2 x}

= \frac{1}{3 x ^{\frac{2}{3}}} (x + 3) + \frac{1}{2 x} 3 x

Simplify

\frac{1}{3 x ^{\frac{2}{3}}} (x + 3) + \frac{1}{2 x} 3 x : \frac{5 x + 6}{6 x ^{\frac{2}{3}}}

= \frac{5 x + 6}{6 x ^{\frac{2}{3}}}

y^{^{''}} + 25 y = 2 sec (5 t)

x \to 0 lim (5^{x})

n = 6 \sum \infty e^{3 - 4 n}

x \to \infty lim (4 x - x^{2})

\frac{\partial}{\partial y} (x^{\frac{3}{2}} - 3 y)

What is the derivative of (\sqrt[3]{x}(sqrt(x)+3)) ?
The derivative of (\sqrt[3]{x}(sqrt(x)+3)) is (5sqrt(x)+6)/(6x^{2/3)}
What is the first derivative of (\sqrt[3]{x}(sqrt(x)+3)) ?
The first derivative of (\sqrt[3]{x}(sqrt(x)+3)) is (5sqrt(x)+6)/(6x^{2/3)}