Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to ω
Find the first partial derivative with respect to r
∂ω∂a=2ωr
Simplify
a=ω2r
Find the first partial derivative by treating the variable r as a constant and differentiating with respect to ω
∂ω∂a=∂ω∂(ω2r)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂ω∂a=r×∂ω∂(ω2)
Use ∂x∂xn=nxn−1 to find derivative
∂ω∂a=r×2ω
Solution
∂ω∂a=2ωr
Show Solution
Solve the equation
Solve for ω
Solve for r
ω=∣r∣arω=−∣r∣ar
Evaluate
a=ω2r
Rewrite the expression
a=rω2
Swap the sides of the equation
rω2=a
Divide both sides
rrω2=ra
Divide the numbers
ω2=ra
Take the root of both sides of the equation and remember to use both positive and negative roots
ω=±ra
Simplify the expression
More Steps
Evaluate
ra
Rewrite the expression
r×rar
Calculate
r2ar
To take a root of a fraction,take the root of the numerator and denominator separately
r2ar
Simplify the radical expression
∣r∣ar
ω=±∣r∣ar
Solution
ω=∣r∣arω=−∣r∣ar
Show Solution