Question

What is dy/dx if y=(x²+2)³(x³+3)²

A.6(x²+2)²(x³+3)
B.2x(x³+3)² +3x² (x² +2)³
C.3(x²+2)²(x³+3)²+2(x²+2)²(x³+3)
D.6x(x²+2)²(x³+3)²+6x²(x²+2)³(x³+3)

D or C I'm not sure ??

Answer 1

first derivative of second * second derivative of first

(x²+2)³ 2(x^3+3)(3x^2)
+
(x³+3)² 3(x^2+2)^2(2x)

which is
6x^2(x^2+2)^3(x^3+3)+6x(x^2+2)^2(x^3+3)^2
which is D

Answer 2

What is dy/dx if y=(x²+2)³(x³+3)²
y'=d/dx 6u^3 v^2=6*3(u^2)vdu/dx+12u^3vdv/dx

where u= (x^2+2) du= 2x dx
v= x^3+3 dv=3x^2 dx

can you take it from there?

Answer 3

Find dy/dx for the following, y=ײ(×+2)³