Posted by Julie on .
Determine the derivative of each function
A1) y = e^x(Sin²x)
A2) y = e²Sin²x
B1) y = (x³ + 1)e^2
B2) y = (x² + 1)e^2
C) y = x²(theta^Sinx)

Calculus grade 12 
Damon,
I am not going to do all these
if y = u(x) v(x)
then dy/dx = u dv/dx + v du/dx
for A1
u = e^x so du/dx = e^x
v = sin^2 x so dv/dx = 2 sin x cos x
so
dy/dx = 2e^x sin x cos x + e^x sin^2 x
= e^x sin x ( 2 cos x + sin x) 
Calculus grade 12 
Julie,
Could you help me for these two:
b) y = (x²+1)e^4
c) y = x²(e^Sinx)
Please & Thank you. 
Calculus grade 12 
Damon,
e^4 is a constant
so
e^4(2x)
x^2 d/dx (e^sin x) + 2 x e^sin x
x^2 (e^sin x)cos x + 2 x e^sin x
x e^sin x [ x cos x + 2 ] 
Calculus grade 12 
Julie,
The answer for b) is e^4(2x) ?
And everything after that is for c) right. So the final answer for c) would be xe^sinx(xcosx + 2)
?
Thankyou. 
Calculus grade 12 
Julie,
In part c) for xcosx could you simplify that or do you keep it as xcosx? Thanks