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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

3 \cdot \frac{( - sin ( x ) ) ( 1 - 2 sin ( x ) ) - ( - 2 cos ( x ) ) cos ( x )}{( 1 - 2 sin ( x ) ) ^{2}} : \frac{3 ( - sin ( x ) ( 1 - 2 sin ( x ) ) + 2 cos ^{2} ( x ) )}{( 1 - 2 sin ( x ) ) ^{2}}

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

\frac{\partial}{\partial v} (\frac{u - v}{3})

\int \frac{e ^{x}}{e ^{x} + 1} d x

3 cos (2 x), (3 - 3 cos (2 x)) x = 0 x = \frac{π}{2}

\int_{0}^{1} π (5 x)^{2} d x

\frac{d}{d x} (5 - 5 x^{2})

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