Given that Y=(x+3)(x+5); find dy/dx
Y=(x+5)(x+3) ............(1)The above expression on the right is a product of two expressions,Hence, product rule differentiation method will be employed as stated below:Y(u,v)=U(x).V(x) .........(2)dy/dx=Udv/dx + V.du/dx ............(3)But comparing (1) and (2) above we have, U=x+3....... (4) V=x+5 ......(5)Therefore by differentiation rule:Y=xn ; dy/dx=nxn-1Applying the above rule to (4) and (5) du/dx=1 .....(6) dv/dx=1 ....(7) Substituting (4) to (7) for (3) we have,dy/dx= (x+3).1 + (x+5).1 ...(8)Simplifying (8) above,dy/dx=x+3 +x+5=2x+8=2(x+4)
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