What is the derivative of $tan (2 x)$ $tan(2x)$ ?

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Answer 1 · 2016-10-26T15:50:35

$\frac{d y}{d x} = 2 {sec}^{2} (2 x)$ $(dy)/(dx)=2sec^2(2x)$

$y = tan (2 x)$ $y=tan(2x)$

$u = 2 x \Rightarrow \frac{d u}{d x} = 2$ $u=2x=>(du)/dx=2$

$y = tan u \Rightarrow \frac{d y}{d u} = {sec}^{2} u$ $y=tanu=>(dy)/(du)=sec^2u$

$\frac{d y}{d x} = \frac{d y}{d u} \times \frac{d u}{d x}$ $(dy)/(dx)=(dy)/(du)xx(du)/(dx)$

$:.(dy)/(dx)=(sec^2u)xx2$

$(dy)/(dx)=2sec^2u=2sec^2(2x)$

What is the derivative of tan(2x)tan(2x)tan(2x)?