Question

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)

Answer 1

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)

Answer 2

Could you help me for these two:

b) y = (x²+1)e^-4
c) y = x²(e^Sinx)

Please & Thank you.

Answer 3

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 ]

Answer 4

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.

Answer 5

In part c) for xcosx could you simplify that or do you keep it as xcosx? Thanks