Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to α
Find the first partial derivative with respect to β
∂α∂a=−2β
Simplify
a=4−2αβ
Find the first partial derivative by treating the variable β as a constant and differentiating with respect to α
∂α∂a=∂α∂(4−2αβ)
Use differentiation rule ∂x∂(f(x)±g(x))=∂x∂(f(x))±∂x∂(g(x))
∂α∂a=∂α∂(4)−∂α∂(2αβ)
Use ∂x∂(c)=0 to find derivative
∂α∂a=0−∂α∂(2αβ)
Evaluate
More Steps
Evaluate
∂α∂(2αβ)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
2β×∂α∂(α)
Use ∂x∂xn=nxn−1 to find derivative
2β×1
Multiply the terms
2β
∂α∂a=0−2β
Solution
∂α∂a=−2β
Show Solution
Solve the equation
Solve for α
Solve for β
α=2β−a+4
Evaluate
a=4−2αβ
Rewrite the expression
a=4−2βα
Swap the sides of the equation
4−2βα=a
Move the constant to the right-hand side and change its sign
−2βα=a−4
Divide both sides
−2β−2βα=−2βa−4
Divide the numbers
α=−2βa−4
Solution
More Steps
Evaluate
−2βa−4
Use b−a=−ba=−ba to rewrite the fraction
−2βa−4
Rewrite the expression
2β−a+4
α=2β−a+4
Show Solution