differentiate the following wr to X

Question

a) x³ - 5x² + e^x + 3 logx

b) x² e^x + logx + 7

c) x²logx÷e^x + x

d) (x² + 1) e^x

e) logx + 1 ÷ x² + 1

f) 1/√4 - x

Answer 1

(a) 3x²-10x+e^x+3/x.

(b) x²e^x+2xe^x+1/x.

(c) [e^x(x²/x+2xlog(x))-x²e^xlog(x)]/e^2x+1=

(x+2xlog(x)-x²log(x))/e^x+1.

(d) (x²+1)e^x+2xe^x.

(e)(i) log(x)+(1/x²)+1: 1/x-2/x³;

   (ii) log(x)+1/(x²+1): 1/x-2x/(x²+1).

(f) 1/√(4-x): ½(4-x)^-3/2, or 1/(2√(4-x)³.