Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to k
Find the first partial derivative with respect to n
∂k∂v=4k3n
Simplify
v=k4n
Find the first partial derivative by treating the variable n as a constant and differentiating with respect to k
∂k∂v=∂k∂(k4n)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂k∂v=n×∂k∂(k4)
Use ∂x∂xn=nxn−1 to find derivative
∂k∂v=n×4k3
Solution
∂k∂v=4k3n
Show Solution
Solve the equation
Solve for k
Solve for n
k=∣n∣4n3vk=−∣n∣4n3v
Evaluate
v=k4n
Rewrite the expression
v=nk4
Swap the sides of the equation
nk4=v
Divide both sides
nnk4=nv
Divide the numbers
k4=nv
Take the root of both sides of the equation and remember to use both positive and negative roots
k=±4nv
Simplify the expression
More Steps
Evaluate
4nv
Rewrite the expression
4n×n3vn3
Use the commutative property to reorder the terms
4n×n3n3v
Calculate
4n4n3v
To take a root of a fraction,take the root of the numerator and denominator separately
4n44n3v
Simplify the radical expression
∣n∣4n3v
k=±∣n∣4n3v
Solution
k=∣n∣4n3vk=−∣n∣4n3v
Show Solution