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

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

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

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

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

sec^{2} (2 x) \cdot 2

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

= sec^{2} (2 x) \cdot 2

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

\frac{x}{x + 1}

\int + \frac{4 y}{1} d y

x \to 2 lim (\frac{1}{( x + 2 )})

\int (\frac{1}{6 x ^{3}}) d x

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