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

The derivative of ((1-cos(x)/(1+cos(x)))^3) is (6sin(x)(1-cos(x))^2)/((1+cos(x))^4)

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

The first derivative of ((1-cos(x)/(1+cos(x)))^3) is (6sin(x)(1-cos(x))^2)/((1+cos(x))^4)

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

\frac{6 sin ( x ) ( 1 - cos ( x ) ) ^{2}}{( 1 + cos ( x ) ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

3 (\frac{1 - cos ( x )}{1 + cos ( x )})^{2} \frac{2 sin ( x )}{( 1 + cos ( x ) ) ^{2}} : \frac{6 sin ( x ) ( 1 - cos ( x ) ) ^{2}}{( 1 + cos ( x ) ) ^{4}}

= \frac{6 sin ( x ) ( 1 - cos ( x ) ) ^{2}}{( 1 + cos ( x ) ) ^{4}}

x \to - 2 - lim (6 x + 5)

\frac{\partial}{\partial y} (x e^{x + y})

x \to 0 lim (\frac{5 - 5 sin ( x )}{x})

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

\int (\frac{3 x}{1 + x ^{4}}) d x

What is the derivative of ((1-cos(x)/(1+cos(x)))^3) ?
The derivative of ((1-cos(x)/(1+cos(x)))^3) is (6sin(x)(1-cos(x))^2)/((1+cos(x))^4)
What is the first derivative of ((1-cos(x)/(1+cos(x)))^3) ?
The first derivative of ((1-cos(x)/(1+cos(x)))^3) is (6sin(x)(1-cos(x))^2)/((1+cos(x))^4)