Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to λ
Find the first partial derivative with respect to μ
∂λ∂h=2λμ
Simplify
h=λ2μ
Find the first partial derivative by treating the variable μ as a constant and differentiating with respect to λ
∂λ∂h=∂λ∂(λ2μ)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂λ∂h=μ×∂λ∂(λ2)
Use ∂x∂xn=nxn−1 to find derivative
∂λ∂h=μ×2λ
Solution
∂λ∂h=2λμ
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Solve the equation
Solve for λ
Solve for μ
λ=∣μ∣μhλ=−∣μ∣μh
Evaluate
h=λ2μ
Rewrite the expression
h=μλ2
Swap the sides of the equation
μλ2=h
Divide both sides
μμλ2=μh
Divide the numbers
λ2=μh
Take the root of both sides of the equation and remember to use both positive and negative roots
λ=±μh
Simplify the expression
More Steps
Evaluate
μh
Rewrite the expression
μ×μhμ
Use the commutative property to reorder the terms
μ×μμh
Calculate
μ2μh
To take a root of a fraction,take the root of the numerator and denominator separately
μ2μh
Simplify the radical expression
∣μ∣μh
λ=±∣μ∣μh
Solution
λ=∣μ∣μhλ=−∣μ∣μh
Show Solution