Question
Function
Find the first partial derivative with respect to q
Find the first partial derivative with respect to w
∂q∂h=2qw
Simplify
h=q2w
Find the first partial derivative by treating the variable w as a constant and differentiating with respect to q
∂q∂h=∂q∂(q2w)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂q∂h=w×∂q∂(q2)
Use ∂x∂xn=nxn−1 to find derivative
∂q∂h=w×2q
Solution
∂q∂h=2qw
Show Solution
Solve the equation
Solve for q
Solve for w
q=∣w∣hwq=−∣w∣hw
Evaluate
h=q2w
Rewrite the expression
h=wq2
Swap the sides of the equation
wq2=h
Divide both sides
wwq2=wh
Divide the numbers
q2=wh
Take the root of both sides of the equation and remember to use both positive and negative roots
q=±wh
Simplify the expression
More Steps
Evaluate
wh
Rewrite the expression
w×whw
Calculate
w2hw
To take a root of a fraction,take the root of the numerator and denominator separately
w2hw
Simplify the radical expression
∣w∣hw
q=±∣w∣hw
Solution
q=∣w∣hwq=−∣w∣hw
Show Solution