# Differentiate with respect to the variable

• August 6th 2007, 09:35 AM
Dean
Differentiate with respect to the variable
Differentiate each of the following with respect to the variable in each case.

(i) $y=8x^{-2}+\frac{5}{x^2}+\frac{7x^3}{3}-6x$

(ii) $y=7e^{-2t}.cos5t$

(iii) $y=ln(2x^2-3x+4)$
• August 6th 2007, 09:54 AM
Krizalid
Use $(x^n)'=nx^{n-1}$

$[f(x)\cdot{g(x)}]^\prime=f'(x)\cdot{g}(x)+f(x)\cdot{g'(x)}$

Also

$(e^u)'=e^u\cdot{u'}$

$(\ln{u})'=\frac1{u}\cdot{u'}$

and $(\cos{kx})'=-k\sin{kx}$