Posted by **Julie** on Friday, April 20, 2012 at 2:57pm.

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**, Friday, April 20, 2012 at 3:09pm
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**, Friday, April 20, 2012 at 4:11pm
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**, Friday, April 20, 2012 at 6:36pm
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**, Friday, April 20, 2012 at 9:33pm
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**, Friday, April 20, 2012 at 9:34pm
In part c) for xcosx could you simplify that or do you keep it as xcosx? Thanks

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