Mathematics Mathematics & Economics Coursework Paper (Coursework Sample)

Mathematics assignment
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Mathematics assignment
Question 1
a.)
d/dx ( 6x2/3y1/4)
Taking y to be a constant
=6y1/4 d/dx(x2/3) applying power rule
=6y1/4. 2/3x2/3-1 simplifying
=4y1/4/x1/3
Second derivative for ( 6x2/3y1/4)
d2/dx2 ( 6x2/3y1/4)
Taking y to be a constant
=4y1/4 d/dx(x-1/3)
Applying power rule
=4y1/4(-1/3x-1/3-1)
Simplifying
= -4y1/4/3x4/3
b.)
Taking y to be a constant
f=e2x, g=x+y2
=d/dx(e2x)( x+y2)+d/dx(x+y2)e2x
Applying chain rule
d/dx(e2x)=e2x.2
Applying chain rule
d/dx(x+y2)=1
Simplifying
=e2x.2(x+y2)+1. e2x
=2 e2x(x+y2)+ e2x
Second derivative
d2/dx2 e2x(x+y2)
Taking y to be a constant
Applying product rule
=d/dx(e2x)(x+y2)+d/dx(x+y2)e2x
=2 e2x(x+y2) + e2x
d/dx(2 e2x(x+y2) + e2x)
Applying sum and difference Rule
=d/dx(2 e2x(x+y2) + d/dx(e2x)