What is the derivative of (x^2/((1+2tan(x)))) ?

The derivative of (x^2/((1+2tan(x)))) is (2x(1+2tan(x))-2sec^2(x)x^2)/((1+2tan(x))^2)

What is the first derivative of (x^2/((1+2tan(x)))) ?

The first derivative of (x^2/((1+2tan(x)))) is (2x(1+2tan(x))-2sec^2(x)x^2)/((1+2tan(x))^2)

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\frac{d}{d x} (\frac{x ^{2}}{( 1 + 2 tan ( x ) )})

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

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{( 1 + 2 tan ( x ) )})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

What is the derivative of (x^2/((1+2tan(x)))) ?
The derivative of (x^2/((1+2tan(x)))) is (2x(1+2tan(x))-2sec^2(x)x^2)/((1+2tan(x))^2)
What is the first derivative of (x^2/((1+2tan(x)))) ?
The first derivative of (x^2/((1+2tan(x)))) is (2x(1+2tan(x))-2sec^2(x)x^2)/((1+2tan(x))^2)