What is the derivative of (3x/(x^3+7x-5)) ?

The derivative of (3x/(x^3+7x-5)) is (3(-2x^3-5))/((x^3+7x-5)^2)

What is the first derivative of (3x/(x^3+7x-5)) ?

The first derivative of (3x/(x^3+7x-5)) is (3(-2x^3-5))/((x^3+7x-5)^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{3 x}{x ^{3} + 7 x - 5})

\frac{3 ( - 2 x ^{3} - 5 )}{( x ^{3} + 7 x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x}{x ^{3} + 7 x - 5})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{x}{x ^{3} + 7 x - 5})

Apply the Quotient Rule:

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

= 3 \cdot \frac{\frac{d x}{d x} ( x ^{3} + 7 x - 5 ) - \frac{d}{d x} ( x ^{3} + 7 x - 5 ) x}{( x ^{3} + 7 x - 5 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{3} + 7 x - 5) = 3 x^{2} + 7

= 3 \cdot \frac{1 \cdot ( x ^{3} + 7 x - 5 ) - ( 3 x ^{2} + 7 ) x}{( x ^{3} + 7 x - 5 ) ^{2}}

Simplify

3 \cdot \frac{1 \cdot ( x ^{3} + 7 x - 5 ) - ( 3 x ^{2} + 7 ) x}{( x ^{3} + 7 x - 5 ) ^{2}} : \frac{3 ( - 2 x ^{3} - 5 )}{( x ^{3} + 7 x - 5 ) ^{2}}

= \frac{3 ( - 2 x ^{3} - 5 )}{( x ^{3} + 7 x - 5 ) ^{2}}

f (x) = lo g_{2} (1 - 3 x)

sin (2 x + π)

y^{^{''}} + 4 y^{^{'}} + 3 y = 4 e^{x}, y (0) = 0, y^{^{'}} (0) = 2

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

\frac{\partial}{\partial x} (cos (y) + y e^{x})

What is the derivative of (3x/(x^3+7x-5)) ?
The derivative of (3x/(x^3+7x-5)) is (3(-2x^3-5))/((x^3+7x-5)^2)
What is the first derivative of (3x/(x^3+7x-5)) ?
The first derivative of (3x/(x^3+7x-5)) is (3(-2x^3-5))/((x^3+7x-5)^2)