en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 1/(2x+5)

Solution

\frac{d}{d x} (\frac{1}{2 x + 5})

Solution

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

Solution steps

\frac{d}{d x} (\frac{1}{2 x + 5})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x + 5) = 2

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

Simplify

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

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

Popular Examples

integral of (cos^2(x))/(1-sin(x))

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

limit as x approaches 2 of 9x

x \to 2 lim (9 x)

tangent of sqrt(5x+6),\at x=2 tangent of

5 x + 6, at x = 2

tangent of y=e^{3x},\at x= 1/3 ln(3)tangent of

y = e^{3 x}, at x = \frac{1}{3} ln (3)

y(x+1)+(dy)/(dx)=0

y (x + 1) + \frac{d y}{d x} = 0

Frequently Asked Questions (FAQ)

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