Question

derivative of x^3 e^(4-x^2)

Answer 1

is that final

Answer 2

do u know how to do that?

Answer 3

do what

Answer 4

\[y=x^3e ^{4-x^2}\]

Answer 5

Take x^3 times the derivative of e^(4-x^2)
Then take e^(4-x^2) times the derivative of x^3

Answer 6

\[x^3(e ^{4-x^2)}(-2x)+e ^{4-x^2}(3x^2)\]

Answer 7

\[e ^{4-x^2}(-2x^4+3x^2)\]

Answer 8

d/dx(e^(4-x^2) x^3)
The product rule, d/dx(u v) = v ( du)/( dx)+u ( dv)/( dx), where u = e^(4-x^2) and v = x^3:
=x3(d/dx(e(4−x2)))+e(4−x2)(d/dx(x3))
Chain rule, d/dx(e^(4-x^2)) = ( de^u)/( du) ( du)/( dx), where u = 4-x^2 and ( de^u)/( du) = e^u:
= x^3 (e^(4-x^2) (d/dx(4-x^2)))+e^(4-x^2) (d/dx(x^3))
derivative of x^3 is 3 x^2:
=e^(4-x^2) x^3 (d/dx(4-x^2))+e^(4-x^2) (3 x^2)
Differentiate the sum term by term and factor out constants:
= e^(4-x^2) x^3 (d/dx(4)-d/dx(x^2))+3 e^(4-x^2) x^2
The derivative of x^2 is 2 x:
= 3 e^(4-x^2) x^2-e^(4-x^2) x^3 (2 x)