What is the derivative of (tan(x-x)/(x^3)) ?

The derivative of (tan(x-x)/(x^3)) is (xtan^2(x)-3(-x+tan(x)))/(x^4)

What is the first derivative of (tan(x-x)/(x^3)) ?

The first derivative of (tan(x-x)/(x^3)) is (xtan^2(x)-3(-x+tan(x)))/(x^4)

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{tan ( x ) - x}{x ^{3}})

\frac{x tan ^{2} ( x ) - 3 ( - x + tan ( x ) )}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{tan ( x ) - x}{x ^{3}})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int x^{3} x^{2} + 18 d x

x \to 4 lim (\frac{x - 4}{∣ x - 4 ∣})

\frac{d}{d x} (2 cos (cot (2 x + 1)))

x \to - 7 + lim (\frac{1}{x + 7})

\int_{2}^{4} 3 e^{3 x} d x

What is the derivative of (tan(x-x)/(x^3)) ?
The derivative of (tan(x-x)/(x^3)) is (xtan^2(x)-3(-x+tan(x)))/(x^4)
What is the first derivative of (tan(x-x)/(x^3)) ?
The first derivative of (tan(x-x)/(x^3)) is (xtan^2(x)-3(-x+tan(x)))/(x^4)