What is the derivative of (1-3e^x/(1-2cos(x))) ?

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

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

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

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

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

Solution steps

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

\frac{d}{d x} (1 - 3 e^{x}) = - 3 e^{x}

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

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

Simplify

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

\frac{\partial}{\partial y} (e^{x y} + 2 x + 3 y)

\int 3 e^{8 x} d x

x \to 0 lim ((1 + 2 x)^{x})

\int \frac{2 x ^{3} - 5}{3 x ^{2}} d x

\int \frac{1}{7 x ( 1 + 7 x )} d x

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