7.1 b) d(2x^2-5)/dx 7.2 e) differentiate log_2|x|+sin(x) f) differentiate 1/(2x)-3*arccos x i) derivative 3*pi^2+6*x^(4/3) 7.3 b) differentiate x^(a)*b^x e) ((sin u) / u - ln u * cos u)' h) differentiate (x*tan(a))/(1+x^2)+x*ln(x) i) differentiate arccos x * arcsin x 7.5 a) 15*t^3*e^t 15 e^t t^2 (t + 3) where t = 1 7.11 b) differentiate sqrt((2x+1)/(4x+1)) d) differentiate cos(-9x+2) + (sin(4x^5))^3 g) differentiate ln(tan(2x))+ln(cot(2x)) j) differentiate arccos x * ln(arctan x) 7.13 differentiate k*sqrt(x/m+a/x) 7.19 b) d^2(q*e^(q^2))/dq^2 c) d^3(t/(2+3t))/dt^3 - d^2(2/(2+3t)^2)/dt^2 7.20 d) differentiate x^3*e^(x^2)*sin(2x) 7.21 d) limit (x^5-1)/(x^3-1) where x to 1 e) limit ln x / sqrt(x) where x to infty f) limit x^2*e^(-x) where x to infty l) limit (x*ln x)/(x+ln x) where x to infty 7.22 c) limit x^2*ln x where x to 0 7.23 b) limit x/sqrt(1+x^2) where x to infty