What is the d/(dq)(((tan(q)))/((1+tan(q)))) ?

The d/(dq)(((tan(q)))/((1+tan(q)))) is 1/(1+sin(2q))

What is the first d/(dq)(((tan(q)))/((1+tan(q)))) ?

The first d/(dq)(((tan(q)))/((1+tan(q)))) is 1/(1+sin(2q))

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\frac{d}{d q} (\frac{( tan ( q ) )}{( 1 + tan ( q ) )})

\frac{1}{1 + sin ( 2 q )}

Solution steps

\frac{d}{d q} (\frac{( tan ( q ) )}{( 1 + tan ( q ) )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d q} ( tan ( q ) ) ( 1 + tan ( q ) ) - \frac{d}{d q} ( 1 + tan ( q ) ) tan ( q )}{( 1 + tan ( q ) ) ^{2}}

\frac{d}{d q} (tan (q)) = sec^{2} (q)

\frac{d}{d q} (1 + tan (q)) = sec^{2} (q)

= \frac{sec ^{2} ( q ) ( 1 + tan ( q ) ) - sec ^{2} ( q ) tan ( q )}{( 1 + tan ( q ) ) ^{2}}

Simplify

\frac{sec ^{2} ( q ) ( 1 + tan ( q ) ) - sec ^{2} ( q ) tan ( q )}{( 1 + tan ( q ) ) ^{2}} : \frac{1}{1 + sin ( 2 q )}

= \frac{1}{1 + sin ( 2 q )}

(e^{x})^{4}

\frac{1}{( x ^{2} + 4 )}

(x^{2} + 3 x)^{15}

f (x) = cos^{3} (3 x - 1)

\frac{900}{x}

What is the d/(dq)(((tan(q)))/((1+tan(q)))) ?
The d/(dq)(((tan(q)))/((1+tan(q)))) is 1/(1+sin(2q))
What is the first d/(dq)(((tan(q)))/((1+tan(q)))) ?
The first d/(dq)(((tan(q)))/((1+tan(q)))) is 1/(1+sin(2q))