What is the derivative of f(x)=(x^2)/((x^3)(x^2)) ?

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

What is the first derivative of f(x)=(x^2)/((x^3)(x^2)) ?

The first derivative of f(x)=(x^2)/((x^3)(x^2)) is -3/(x^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

f (x) = \frac{x ^{2}}{( x ^{3} ) ( x ^{2} )}

- \frac{3}{x ^{4}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

= \frac{2 x x ^{3} x ^{2} - 5 x ^{4} x ^{2}}{( x ^{3} x ^{2} ) ^{2}}

Simplify

\frac{2 x x ^{3} x ^{2} - 5 x ^{4} x ^{2}}{( x ^{3} x ^{2} ) ^{2}} : - \frac{3}{x ^{4}}

= - \frac{3}{x ^{4}}

What is the derivative of f(x)=(x^2)/((x^3)(x^2)) ?
The derivative of f(x)=(x^2)/((x^3)(x^2)) is -3/(x^4)
What is the first derivative of f(x)=(x^2)/((x^3)(x^2)) ?
The first derivative of f(x)=(x^2)/((x^3)(x^2)) is -3/(x^4)