What is the derivative of $tan(5x)^(1/2)$ ?

Question

2309 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-27T08:13:09

$(dy)/(dx)=sqrt5/2(x^(-1/2))sec^2(5x)^(1/2)$

$y=tan(5x)^(1/2)$

$u=(5x)^(1/2)=5^(1/2)x^(1/2)$

$=>(dy)/(du)=5^(1/2)1/2x^(-1/2)=sqrt5/2(x^(-1/2))$

$y=tanu=>(dy)/(du)=sec^2u$

$(dy)/(dx)=(dy)/(du)xx(du)/(dx)$

$:.(dy)/(dx)=sec^2uxxsqrt5/2(x^(-1/2))$

$:.(dy)/(dx)=sqrt5/2(x^(-1/2))sec^2(5x)^(1/2)$

What is the derivative of tan(5x)^(1/2)tan(5x)^(1/2)?