differentiate with respect to x ax^2+2hyx+by^2

Question

differentiate with respect to x

ax^2+2hyx+by^2

Answer 1

To differentiate wrt to X

 

aX^2 +2hYX +bY^2

a*2*X + 2h( Y + X dY/dX) +2bY * dY/dX

He we assumed both X and Y are variables and a, b and h are constants

Answer 2

Are you asking for the partial derivative or the total derivative?  If you want the partial derivative with respect to x (i.e. ∂/∂x), then treat y as if it was a constant, and get

 

∂/∂x (ax²+2hyx+by²) = 2ax + 2hy

 

But if y = f(x) and you want the total derivative with respect to x (i.e. d/dx), then

 

d/dx (ax²+2hyx+by²) = 2ax +2hy +2hx(dy/dx) + 2by(dydx)

Answer 3

Differentiating in terms of a single variable means to treat all the rest of the variables as if they were numbers.

 

So do you know how to differentiate 5x² +3x +2?  You'd get 10x + 3.

 

So your first term ax² would become 2ax

your second term would become 2hy

and your third term would disappear entirely.

 

So your answer would be 2ax + 2hy.

 

Hope this helped.