# `E (a,b,c,d) =ac^2+cb^2+5d+5a ` Part. diff. `(delE)/(del a), (delE)/(delb), (delE)/(delc), (delE)/(deld)`

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate partial derivative `(del E)/(del a),`  hence, you need to differentiate the function with respect to a, considering b,c,d as constants, such that:

`(del E)/(del a) = c^2 + 5`

You need to evaluate partial derivative `(del E)/(del b), ` hence, you need to differentiate the function with respect to b, considering a,c,d as constants, such that:

`(del E)/(del b) = 2bc`

You need to evaluate partial derivative `(del E)/(del c), ` hence, you need to differentiate the function with respect to c, considering a,b,d as constants, such that:

`(del E)/(del c) = 2ac + b^2`

You need to evaluate partial derivative `(del E)/(del d),`  hence, you need to differentiate the function with respect to d, considering a,b,c as constants, such that:

`(del E)/(del d)= 5`

Hence, evaluating the partial derivatives yields `(del E)/(del a) = c^2 + 5, (del E)/(del b) = 2bc, (del E)/(del c) = 2ac + b^2, (del E)/(del d) = 5.`