Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to m
Find the first partial derivative with respect to ω
∂m∂k=ω2
Simplify
k=mω2
Find the first partial derivative by treating the variable ω as a constant and differentiating with respect to m
∂m∂k=∂m∂(mω2)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂m∂k=ω2×∂m∂(m)
Use ∂x∂xn=nxn−1 to find derivative
∂m∂k=ω2×1
Solution
∂m∂k=ω2
Show Solution
Solve the equation
Solve for ω
Solve for k
Solve for m
ω=∣m∣kmω=−∣m∣km
Evaluate
k=mω2
Swap the sides of the equation
mω2=k
Divide both sides
mmω2=mk
Divide the numbers
ω2=mk
Take the root of both sides of the equation and remember to use both positive and negative roots
ω=±mk
Simplify the expression
More Steps
Evaluate
mk
Rewrite the expression
m×mkm
Calculate
m2km
To take a root of a fraction,take the root of the numerator and denominator separately
m2km
Simplify the radical expression
∣m∣km
ω=±∣m∣km
Solution
ω=∣m∣kmω=−∣m∣km
Show Solution