Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to p
Find the first partial derivative with respect to q
∂p∂z=2pq2
Simplify
z=p2q2
Find the first partial derivative by treating the variable q as a constant and differentiating with respect to p
∂p∂z=∂p∂(p2q2)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂p∂z=q2×∂p∂(p2)
Use ∂x∂xn=nxn−1 to find derivative
∂p∂z=q2×2p
Solution
∂p∂z=2pq2
Show Solution
Solve the equation
Solve for p
Solve for q
p=∣q∣zp=−∣q∣z
Evaluate
z=p2q2
Rewrite the expression
z=q2p2
Swap the sides of the equation
q2p2=z
Divide both sides
q2q2p2=q2z
Divide the numbers
p2=q2z
Take the root of both sides of the equation and remember to use both positive and negative roots
p=±q2z
Simplify the expression
More Steps
Evaluate
q2z
To take a root of a fraction,take the root of the numerator and denominator separately
q2z
Simplify the radical expression
∣q∣z
p=±∣q∣z
Solution
p=∣q∣zp=−∣q∣z
Show Solution