posted by .

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)

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)

Could you help me for these two:

b) y = (x²+1)e^-4
c) y = x²(e^Sinx)

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 ]

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.

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

## Similar Questions

1. ### Calculus

I need to find the slope of the graph of the function at the given point. Function: f(theta)=4sin(theta)-(theta) Point: (0,0) I tried finding the derivative of the function at theta=0, but I got 0 for an answer. I checked the answer …
2. ### calculus

Could someone check my reasoning? thanx Find the derivative of the function. sin(sin[sinx]) I need to use the chain rule to solve. So I take the derivative sin(sin[sinx) first. Then multiply that by the inside which is the derivative

Determine the derivative of the function (² = square): a) y = (x² + x - 1)Sin²x b) y = (x² + 1)/Sin²x

a) determine the derivative of y = sin2x b) determine the derivative of y = 2SinxCosx c) shoe that derivatives in parts a) and b) are equal d) explain why derivatives in parts a) and be should be equal.

solve for (<_ = less than or equal to / pie = pie sign / -pie = negative pie) 3 sin²x = cos²x ; 0 <_ x < 2pie cos²x - sin²x = sinx ; -pie < x <_ pie

Determine the equation of the tangent line to the function f(x) = x + Sinx at x = pie
7. ### Calculus

Find the derivative of each 1) y = e^x(Sin²x) 2) y = (x²+1)e^-4 3) y = x²(e^Sinx)