Assignment $1($Differentiations$)$

Using definition, compute the derivative function of $f(x)$ below:

$f(x)=\frac{3}{x+1}$

$f(t)=\sqrt[\phantom{2}]{3t+1}$

Evaluate $f^{\text{'}}(x)$ for the following functions by using rules of differentiations.

$3.h(x)=\frac{10}{\sqrt[3]{x}}-2(3x^2-\sqrt[\phantom{2}]{x})+x$

$4.f(x)=(15x^2-\frac{3}{x})\frac{x^2-1}{x^3+6\sqrt[\phantom{2}]{x}}$

$5.g(x)=\sqrt[\phantom{2}]{(x^2+1{)}^{-4}(\sqrt[\phantom{2}]{x}+1{)}^3}$

$6.f(t)=ln(sin3t+\frac{4\sqrt[\phantom{2}]{t^2+1}}{t-5}{)}^3$

$7.f(x)=\frac{sec(x^2)ta{n}^2(x^2)}{csc\sqrt[\phantom{2}]{4x}}$

$8.f(x)=(\frac{1}{e}{)}^{2x}cos4x$

$9.f(x)=4tan(ln(3x^2+2))e^{x^2+tan4x}$

$10.f(x)=ln[ln\sqrt[\phantom{2}]{cos8x}].sec(ta{n}^{2}x)$

$11.f(x)=sin[sin(ln{x}^2)]*se{c}^2(tanx)$

$12.f(x)=csc(\sqrt[3]{e^{2x}{x}^3})$