What is the derivative of (8sqrt(5))/(15)x^{3/2}-2 ?

The derivative of (8sqrt(5))/(15)x^{3/2}-2 is (4x^{1/2})/(5^{1/2)}

What is the first derivative of (8sqrt(5))/(15)x^{3/2}-2 ?

The first derivative of (8sqrt(5))/(15)x^{3/2}-2 is (4x^{1/2})/(5^{1/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{8 5}{15} x^{\frac{3}{2}} - 2

\frac{4 x ^{\frac{1}{2}}}{5 ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (\frac{8 5}{15} x^{\frac{3}{2}} - 2)

Simplify

\frac{8 5}{15} x^{\frac{3}{2}} - 2 : \frac{8 x ^{\frac{3}{2}}}{3 \cdot 5 ^{\frac{1}{2}}} - 2

= \frac{d}{d x} (\frac{8 x ^{\frac{3}{2}}}{3 \cdot 5 ^{\frac{1}{2}}} - 2)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{8 x ^{\frac{3}{2}}}{3 \cdot 5 ^{\frac{1}{2}}}) - \frac{d}{d x} (2)

\frac{d}{d x} (\frac{8 x ^{\frac{3}{2}}}{3 \cdot 5 ^{\frac{1}{2}}}) = \frac{4 x ^{\frac{1}{2}}}{5 ^{\frac{1}{2}}}

\frac{d}{d x} (2) = 0

= \frac{4 x ^{\frac{1}{2}}}{5 ^{\frac{1}{2}}} - 0

Simplify

= \frac{4 x ^{\frac{1}{2}}}{5 ^{\frac{1}{2}}}

What is the derivative of (8sqrt(5))/(15)x^{3/2}-2 ?
The derivative of (8sqrt(5))/(15)x^{3/2}-2 is (4x^{1/2})/(5^{1/2)}
What is the first derivative of (8sqrt(5))/(15)x^{3/2}-2 ?
The first derivative of (8sqrt(5))/(15)x^{3/2}-2 is (4x^{1/2})/(5^{1/2)}