Question
Function
Find the first partial derivative with respect to a
Find the first partial derivative with respect to b
∂a∂s=7
Simplify
s=7a−3b
Find the first partial derivative by treating the variable b as a constant and differentiating with respect to a
∂a∂s=∂a∂(7a−3b)
Use differentiation rule ∂x∂(f(x)±g(x))=∂x∂(f(x))±∂x∂(g(x))
∂a∂s=∂a∂(7a)−∂a∂(3b)
Evaluate
More Steps

Evaluate
∂a∂(7a)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
7×∂a∂(a)
Use ∂x∂xn=nxn−1 to find derivative
7×1
Multiply the terms
7
∂a∂s=7−∂a∂(3b)
Use ∂x∂(c)=0 to find derivative
∂a∂s=7−0
Solution
∂a∂s=7
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Solve the equation
Solve for a
Solve for b
a=7s+3b
Evaluate
s=7a−3b
Swap the sides of the equation
7a−3b=s
Move the expression to the right-hand side and change its sign
7a=s+3b
Divide both sides
77a=7s+3b
Solution
a=7s+3b
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