Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to h
Find the first partial derivative with respect to y
∂h∂z=18hy2
Evaluate
z=h2×9y2
Use the commutative property to reorder the terms
z=9h2y2
Find the first partial derivative by treating the variable y as a constant and differentiating with respect to h
∂h∂z=∂h∂(9h2y2)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂h∂z=9y2×∂h∂(h2)
Use ∂x∂xn=nxn−1 to find derivative
∂h∂z=9y2×2h
Solution
∂h∂z=18hy2
Show Solution
Solve the equation
Solve for h
Solve for y
Solve for z
h=3∣y∣zh=−3∣y∣z
Evaluate
z=h2×9y2
Use the commutative property to reorder the terms
z=9h2y2
Rewrite the expression
z=9y2h2
Swap the sides of the equation
9y2h2=z
Divide both sides
9y29y2h2=9y2z
Divide the numbers
h2=9y2z
Take the root of both sides of the equation and remember to use both positive and negative roots
h=±9y2z
Simplify the expression
More Steps
Evaluate
9y2z
To take a root of a fraction,take the root of the numerator and denominator separately
9y2z
Simplify the radical expression
More Steps
Evaluate
9y2
Rewrite the expression
9×y2
Simplify the root
3∣y∣
3∣y∣z
h=±3∣y∣z
Solution
h=3∣y∣zh=−3∣y∣z
Show Solution