What is the derivative of (2x(sin(x))/(x^3-1)) ?

The derivative of (2x(sin(x))/(x^3-1)) is (2(x^4cos(x)-2x^3sin(x)-xcos(x)-sin(x)))/((x^3-1)^2)

What is the first derivative of (2x(sin(x))/(x^3-1)) ?

The first derivative of (2x(sin(x))/(x^3-1)) is (2(x^4cos(x)-2x^3sin(x)-xcos(x)-sin(x)))/((x^3-1)^2)

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{2 x ( sin ( x ) )}{x ^{3} - 1})

\frac{2 ( x ^{4} cos ( x ) - 2 x ^{3} sin ( x ) - x cos ( x ) - sin ( x ) )}{( x ^{3} - 1 ) ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x sin (x)) = sin (x) + x cos (x)

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

= 2 \cdot \frac{( sin ( x ) + x cos ( x ) ) ( x ^{3} - 1 ) - 3 x ^{2} x sin ( x )}{( x ^{3} - 1 ) ^{2}}

Simplify

2 \cdot \frac{( sin ( x ) + x cos ( x ) ) ( x ^{3} - 1 ) - 3 x ^{2} x sin ( x )}{( x ^{3} - 1 ) ^{2}} : \frac{2 ( x ^{4} cos ( x ) - 2 x ^{3} sin ( x ) - x cos ( x ) - sin ( x ) )}{( x ^{3} - 1 ) ^{2}}

= \frac{2 ( x ^{4} cos ( x ) - 2 x ^{3} sin ( x ) - x cos ( x ) - sin ( x ) )}{( x ^{3} - 1 ) ^{2}}

\int \frac{2}{9 + x ^{2}} d x

y = x + \frac{5}{x}

\frac{d}{d x} (- \frac{36}{x ^{4}})

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

\int (cot (b x) + tan (b x))^{2} d x

What is the derivative of (2x(sin(x))/(x^3-1)) ?
The derivative of (2x(sin(x))/(x^3-1)) is (2(x^4cos(x)-2x^3sin(x)-xcos(x)-sin(x)))/((x^3-1)^2)
What is the first derivative of (2x(sin(x))/(x^3-1)) ?
The first derivative of (2x(sin(x))/(x^3-1)) is (2(x^4cos(x)-2x^3sin(x)-xcos(x)-sin(x)))/((x^3-1)^2)