What is the derivative of (sin(x)/(2cos^2(x))) ?

The derivative of (sin(x)/(2cos^2(x))) is (cos^3(x)+sin(2x)sin(x))/(2cos^4(x))

What is the first derivative of (sin(x)/(2cos^2(x))) ?

The first derivative of (sin(x)/(2cos^2(x))) is (cos^3(x)+sin(2x)sin(x))/(2cos^4(x))

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\frac{d}{d x} (\frac{sin ( x )}{2 cos ^{2} ( x )})

\frac{cos ^{3} ( x ) + sin ( 2 x ) sin ( x )}{2 cos ^{4} ( x )}

Solution steps

\frac{d}{d x} (\frac{sin ( x )}{2 cos ^{2} ( x )})

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1}{2} \cdot \frac{cos ( x ) cos ^{2} ( x ) - ( - sin ( 2 x ) ) sin ( x )}{( cos ^{2} ( x ) ) ^{2}} : \frac{cos ^{3} ( x ) + sin ( 2 x ) sin ( x )}{2 cos ^{4} ( x )}

= \frac{cos ^{3} ( x ) + sin ( 2 x ) sin ( x )}{2 cos ^{4} ( x )}

What is the derivative of (sin(x)/(2cos^2(x))) ?
The derivative of (sin(x)/(2cos^2(x))) is (cos^3(x)+sin(2x)sin(x))/(2cos^4(x))
What is the first derivative of (sin(x)/(2cos^2(x))) ?
The first derivative of (sin(x)/(2cos^2(x))) is (cos^3(x)+sin(2x)sin(x))/(2cos^4(x))