Hi

I need help on the following questions:

1)Prove that: $\displaystyle \frac{d}{dx}(arctan(x)) = \frac{1}{1+x^2}$

This is what i have done:

$\displaystyle x= tan(y)$

$\displaystyle \frac{dy}{dx} = \frac{1}{\frac{dy}{dx}} = \frac{1}{sec^2(y)}

$

$\displaystyle sec^2(y) = \frac{1}{cos^2(y)}$

$\displaystyle = \sqrt{1 - sin^2y}$ stuck at this part

2) Find the derivative of $\displaystyle arcsin(\frac{2x}{3})$

This is what i have done:

$\displaystyle \frac{\frac{2}{3}}{\sqrt{1-\frac{4x^2}{9}}}$

$\displaystyle \frac{2}{3\sqrt{1-\frac{4x^2}{9}}}$

3) Find the derivative of $\displaystyle e^{-2x}sinh(5x)$

$\displaystyle \frac{dy}{dx} = \frac{e^{x}xcosh(x) + sinh(x) - xsinhx * e^{x}}{(e^x)^2}$

$\displaystyle \frac{dy}{dx} = \frac{e^{x}(xcosh(x) + sinh(x) - xsinhx)}{(e^x)^2}$

What have i done wrong??

P.S