en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (1-3x/(5+x))

Solution

\frac{d}{d x} (\frac{1 - 3 x}{5 + x})

Solution

- \frac{16}{( 5 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 - 3 x}{5 + x})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (5 + x) = 1

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

Simplify

\frac{( - 3 ) ( 5 + x ) - 1 \cdot ( 1 - 3 x )}{( 5 + x ) ^{2}} : - \frac{16}{( 5 + x ) ^{2}}

= - \frac{16}{( 5 + x ) ^{2}}

Popular Examples

integral of t^6(3+t^7)^6

\int t^{6} (3 + t^{7})^{6} d t

(\partial)/(\partial x)(-e^{cos(x)}sin(x))

\frac{\partial}{\partial x} (- e^{c o s (x)} sin (x))

derivative of 100x^{0.25}y^{0.75}

\frac{d}{d x} (100 x^{0.25} y^{0.75})

integral from-1 to 1 of (e^x-(x^2-2))

\int_{- 1}^{1} (e^{x} - (x^{2} - 2)) d x

(dy)/(dx)= 1/(xln(2))

\frac{d y}{d x} = \frac{1}{x ln ( 2 )}

Frequently Asked Questions (FAQ)

What is the derivative of (1-3x/(5+x)) ?
The derivative of (1-3x/(5+x)) is -(16)/((5+x)^2)
What is the first derivative of (1-3x/(5+x)) ?
The first derivative of (1-3x/(5+x)) is -(16)/((5+x)^2)