What is the derivative of cos^3(x/(x+1)) ?

The derivative of cos^3(x/(x+1)) is -(3cos^2(x/(x+1))sin(x/(x+1)))/((x+1)^2)

What is the first derivative of cos^3(x/(x+1)) ?

The first derivative of cos^3(x/(x+1)) is -(3cos^2(x/(x+1))sin(x/(x+1)))/((x+1)^2)

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\frac{d}{d x} (cos^{3} (\frac{x}{x + 1}))

- \frac{3 cos ^{2} ( \frac{x}{x + 1} ) sin ( \frac{x}{x + 1} )}{( x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (cos^{3} (\frac{x}{x + 1}))

Apply the chain rule:

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

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

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

= 3 (cos (\frac{x}{x + 1}))^{2} (- \frac{sin ( \frac{x}{x + 1} )}{( x + 1 ) ^{2}})

Simplify

3 cos^{2} (\frac{x}{x + 1}) (- \frac{sin ( \frac{x}{x + 1} )}{( x + 1 ) ^{2}}) : - \frac{3 cos ^{2} ( \frac{x}{x + 1} ) sin ( \frac{x}{x + 1} )}{( x + 1 ) ^{2}}

= - \frac{3 cos ^{2} ( \frac{x}{x + 1} ) sin ( \frac{x}{x + 1} )}{( x + 1 ) ^{2}}

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