When a=3
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When a=3.5, b=1.8, c=1.5, d=1.25, x=0.6
A variable u is a function of x. A second order accurate finite difference approximation for ∂u/∂x at x = xi is:
(equation 2.1) = (????????/????????????) = ((????????+1) − (????????−1))/2????????
where ?x denotes the increment between points xi-1, xi, xi+1 etc.
For the function: ???? = ????????????????(????????) + ????????????????????
where a, b, c, d, x should be chosen according to your case in above:
- Determine ∂u/∂x for your values of a, b, c, d, x by differentiating u.
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∂u/∂x=0.0007908602331
Step-by-step explanation
u=acos?(bx)+cxedx
a=3.5, b=1.8, c=1.5, d=1.25
u=3.5cos?(1.8x)+1.5xe1.25x
∂u/∂x=3.5[-sin(1.8x)](1.8)+1.5[(1)e1.25x+x(e1.25x)(1.25)]
∂u/∂x=-6.3 sin?(1.8x)+(1.5+1.875x)e1.25x
x=0.6
∂u/∂x=-6.3 sin?[1.8(0.6)]+[1.5+1.875(0.6)]e1.25(0.6)
∂u/∂x=0.0007908602331
