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Popular >

derivative of cos(x/(x+1))

Solution

derivative of

cos (\frac{x}{x + 1})

Solution

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

Solution steps

\frac{d}{d x} (cos (\frac{x}{x + 1}))

Apply the chain rule:

- sin (\frac{x}{x + 1}) \frac{d}{d x} (\frac{x}{x + 1})

= - sin (\frac{x}{x + 1}) \frac{d}{d x} (\frac{x}{x + 1})

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

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

Simplify

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

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

Popular Examples

derivative of 1+2xy derivative of

1 + 2 x y

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derivative of sin^2(x)+tan^3(x)derivative of

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d/(dt)((500)/((t+2))-(1000)/(((t+2)^2)))

\frac{d}{d t} \frac{500}{( t + 2 )} - \frac{1000}{( ( t + 2 ) ^{2} )}

derivative of (x^2)/((e^x-1)^2)derivative of

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

Frequently Asked Questions (FAQ)

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