What is the derivative of (1-2e^x/(1-2cos(x))) ?

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

(x + 1) y^{^{'}} = x^{2} - y

\int \frac{9}{x ^{2} + 1} d x

(\frac{x}{1 - x})^{^{'}}

y^{^{''}} - 8 y^{^{'}} + 20 y = 200 x^{2} - 52 x e^{x}

\frac{\partial}{\partial x} (7 x + 6 y + 7 x y)

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