What is the derivative of (x^{7/3}+3x^3-8/(6x^2)) ?

The derivative of (x^{7/3}+3x^3-8/(6x^2)) is (9x^3+x^{7/3}+48)/(18x^3)

What is the first derivative of (x^{7/3}+3x^3-8/(6x^2)) ?

The first derivative of (x^{7/3}+3x^3-8/(6x^2)) is (9x^3+x^{7/3}+48)/(18x^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{x ^{\frac{7}{3}} + 3 x ^{3} - 8}{6 x ^{2}})

\frac{9 x ^{3} + x ^{\frac{7}{3}} + 48}{18 x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{\frac{7}{3}} + 3 x ^{3} - 8}{6 x ^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{6} \frac{d}{d x} (\frac{x ^{\frac{7}{3}} + 3 x ^{3} - 8}{x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{6} \cdot \frac{\frac{d}{d x} ( x ^{\frac{7}{3}} + 3 x ^{3} - 8 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x ^{\frac{7}{3}} + 3 x ^{3} - 8 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (x^{\frac{7}{3}} + 3 x^{3} - 8) = 9 x^{2} + \frac{7 x ^{\frac{4}{3}}}{3}

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

= \frac{1}{6} \cdot \frac{( 9 x ^{2} + \frac{7 x ^{\frac{4}{3}}}{3} ) x ^{2} - 2 x ( x ^{\frac{7}{3}} + 3 x ^{3} - 8 )}{( x ^{2} ) ^{2}}

Simplify

\frac{1}{6} \cdot \frac{( 9 x ^{2} + \frac{7 x ^{\frac{4}{3}}}{3} ) x ^{2} - 2 x ( x ^{\frac{7}{3}} + 3 x ^{3} - 8 )}{( x ^{2} ) ^{2}} : \frac{9 x ^{3} + x ^{\frac{7}{3}} + 48}{18 x ^{3}}

= \frac{9 x ^{3} + x ^{\frac{7}{3}} + 48}{18 x ^{3}}

x \to 0 lim (\frac{x + tan ( x )}{x})

\frac{d}{d x} (x^{v})

\int \frac{1 + x + x ^{2}}{x} d x

\int \frac{ln ( x )}{x ^{a}} d x

\int \frac{( 3 x ^{2} + 2 )}{x - 1} d x

What is the derivative of (x^{7/3}+3x^3-8/(6x^2)) ?
The derivative of (x^{7/3}+3x^3-8/(6x^2)) is (9x^3+x^{7/3}+48)/(18x^3)
What is the first derivative of (x^{7/3}+3x^3-8/(6x^2)) ?
The first derivative of (x^{7/3}+3x^3-8/(6x^2)) is (9x^3+x^{7/3}+48)/(18x^3)