Which order of differentiation will calculate f xy faster :x first or y first? t

Question

Which order of differentiation will calculate fxy faster :x first or y first? try to answer without writing anything down.

a) f(x,y)= xsiny+ey

c) f(x,y) = y+(x/y)

d)f(x,y)= y+x2y+4y3-ln(y2+1)

e)f(x,y)=x2+5xy+sinx+7ex

f) f(x,y)= xlnxy

a) Which order of differentiation will calculate fxy faster for f(x,y)= xsiny+ey?

y first or x first?

b) Which order of differentiation will calculate fxy faster for f(x,y)= 1/x?

y first or x first?

c) Which order of differentiation will calculate fxy faster for f(x,y)=  y+(x/y)?

y first or x first?

d) Which order of differentiation will calculate fxy faster for f(x,y)= y+x2y+4y3-ln(y2+1)?

y first or x first?

e)Which order of differentiation will calculate fxy faster for f(x,y)=x2+5xy+sinx+7ex?

y first or x first?

f) Which order of differentiation will calculate fxy faster for f(x,y)=x ln xy?

y first or x first?

Which order of differentiation will calculate fxy faster :x first or y first? try to answer without writing anything down. a) f(x,y)= xsiny+ey b) f(x,y)=1/x c) f(x,y) = y+(x/y) d)f(x,y)= y+x2y+4y3-ln(y2+1) e)f(x,y)=x2+5xy+sinx+7ex f) f(x,y)= xlnxy a) Which order of differentiation will calculate fxy faster for f(x,y)= xsiny+ey? y first or x first? b) Which order of differentiation will calculate fxy faster for f(x,y)= 1/x? y first or x first? c) Which order of differentiation will calculate fxy faster for f(x,y)= y+(x/y)? y first or x first? d) Which order of differentiation will calculate fxy faster for f(x,y)= y+x2y+4y3-ln(y2+1)? y first or x first? e)Which order of differentiation will calculate fxy faster for f(x,y)=x2+5xy+sinx+7ex? y first or x first? f) Which order of differentiation will calculate fxy faster for f(x,y)=x ln xy? y first or x first?

Explanation / Answer

a). First differentiate with respect to x then y. As differentiating with respect to x will remove the x term.

b). here first differentiate with respect to x then y. As y term is missing.

c).  First differentiate with respect to x then y. As differentiating with respect to x will remove the x term.

d).  First differentiate with respect to x then y. As differentiating with respect to x will simplify the expression a bit.

e).  First differentiate with respect to y then x. As differentiating with respect to y will remove the y term.

f).   First differentiate with respect to y then x. As differentiating with respect to y will simplify the expression a bit.

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