Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to r
Find the first partial derivative with respect to θ
∂r∂a=rθ
Simplify
a=21r2θ
Find the first partial derivative by treating the variable θ as a constant and differentiating with respect to r
∂r∂a=∂r∂(21r2θ)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂r∂a=21θ×∂r∂(r2)
Use ∂x∂xn=nxn−1 to find derivative
∂r∂a=21θ×2r
Solution
∂r∂a=rθ
Show Solution
Solve the equation
Solve for θ
Solve for r
θ=r22a
Evaluate
a=21r2θ
Swap the sides of the equation
21r2θ=a
Divide both sides
21r221r2θ=21r2a
Divide the numbers
θ=21r2a
Solution
More Steps
Evaluate
21r2a
Multiply by the reciprocal
a×r22
Multiply the numbers
r2a×2
Multiply the numbers
r22a
θ=r22a
Show Solution