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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

2 \cdot \frac{cos ( x )}{1 + sin ( x )} \frac{d}{d x} (\frac{cos ( x )}{1 + sin ( x )})

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

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

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

Simplify

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

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

\int \frac{3}{2} x^{3} d x

3 x^{2} ln (x), 12 ln (x)

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

\frac{\partial}{\partial x} (6 y^{2} - 4 y^{3} - 3 x^{2} + 6 x y)

f (x) = \frac{6}{5 x + 2}, at x = - 1

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