en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 1/(2-cos(pix))

Solution

\frac{d}{d x} (\frac{1}{2 - cos ( π ) x})

Solution

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

Solution steps

\frac{d}{d x} (\frac{1}{2 - cos ( π ) x})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 - cos (π) x) = 1

= - \frac{1}{( 2 - cos ( π ) x ) ^{2}} \cdot 1

Simplify

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

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

Popular Examples

limit as x approaches-6+of 1/((x+6)^4)

x \to - 6 + lim (\frac{1}{( x + 6 ) ^{4}})

- 2 y^{2} d y = y^{3} v d v

limit as x approaches 4 of (5x+7)^4

x \to 4 lim ((5 x + 7)^{4})

integral of (4x^3+2x^2+8)/((x^2+4)^2)

\int \frac{4 x ^{3} + 2 x ^{2} + 8}{( x ^{2} + 4 ) ^{2}} d x

derivative of ((ln(x)^2)/(e^x))

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

Frequently Asked Questions (FAQ)

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