What is the derivative of (1-4e^x/(1-5cos(x))) ?

The derivative of (1-4e^x/(1-5cos(x))) is (-4e^x(1-5cos(x))-5sin(x)(1-4e^x))/((1-5cos(x))^2)

What is the first derivative of (1-4e^x/(1-5cos(x))) ?

The first derivative of (1-4e^x/(1-5cos(x))) is (-4e^x(1-5cos(x))-5sin(x)(1-4e^x))/((1-5cos(x))^2)

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\frac{d}{d x} (\frac{1 - 4 e ^{x}}{1 - 5 cos ( x )})

\frac{- 4 e ^{x} ( 1 - 5 cos ( x ) ) - 5 sin ( x ) ( 1 - 4 e ^{x} )}{( 1 - 5 cos ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 - 4 e ^{x}}{1 - 5 cos ( x )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 1 - 4 e ^{x} ) ( 1 - 5 cos ( x ) ) - \frac{d}{d x} ( 1 - 5 cos ( x ) ) ( 1 - 4 e ^{x} )}{( 1 - 5 cos ( x ) ) ^{2}}

\frac{d}{d x} (1 - 4 e^{x}) = - 4 e^{x}

\frac{d}{d x} (1 - 5 cos (x)) = 5 sin (x)

= \frac{( - 4 e ^{x} ) ( 1 - 5 cos ( x ) ) - 5 sin ( x ) ( 1 - 4 e ^{x} )}{( 1 - 5 cos ( x ) ) ^{2}}

Simplify

= \frac{- 4 e ^{x} ( 1 - 5 cos ( x ) ) - 5 sin ( x ) ( 1 - 4 e ^{x} )}{( 1 - 5 cos ( x ) ) ^{2}}

f (x) = \frac{1}{2} arctan (\frac{x}{2})

\frac{d}{d x} (6 x^{2} - 96 x)

\int (2 x + 1)^{4} d x

\int_{0}^{8} 2 t^{2} - 24 t + 70 d t

y^{^{'}} = \frac{1 + y ^{2}}{1 + x ^{2}}

What is the derivative of (1-4e^x/(1-5cos(x))) ?
The derivative of (1-4e^x/(1-5cos(x))) is (-4e^x(1-5cos(x))-5sin(x)(1-4e^x))/((1-5cos(x))^2)
What is the first derivative of (1-4e^x/(1-5cos(x))) ?
The first derivative of (1-4e^x/(1-5cos(x))) is (-4e^x(1-5cos(x))-5sin(x)(1-4e^x))/((1-5cos(x))^2)