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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

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

y (θ) = arctan (cos (θ))

\int x (2 - x)^{2} d x

\int_{0}^{5} x 1 + x d x

e^{x^{3} + 2 x}

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