Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to k
Find the first partial derivative with respect to x
∂k∂y=xx
Simplify
y=kxx
Find the first partial derivative by treating the variable x as a constant and differentiating with respect to k
∂k∂y=∂k∂(kxx)
Use differentiation rule ∂x∂(f(x)×g(x))=∂x∂(f(x))×g(x)+f(x)×∂x∂(g(x))
∂k∂y=∂k∂(kx)x+kx×∂k∂(x)
Evaluate
More Steps
Evaluate
∂k∂(kx)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
x×∂k∂(k)
Use ∂x∂xn=nxn−1 to find derivative
x×1
Multiply the terms
x
∂k∂y=xx+kx×∂k∂(x)
Use ∂x∂(c)=0 to find derivative
∂k∂y=xx+kx×0
Evaluate
∂k∂y=xx+0
Solution
∂k∂y=xx
Show Solution
Solve the equation
Solve for x
Solve for k
x=k3ky2
Evaluate
y=kxx
Swap the sides of the equation
kxx=y
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(kxx)2=y2
Evaluate the power
k2x3=y2
Divide both sides
k2k2x3=k2y2
Divide the numbers
x3=k2y2
Take the 3-th root on both sides of the equation
3x3=3k2y2
Calculate
x=3k2y2
Solution
More Steps
Evaluate
3k2y2
To take a root of a fraction,take the root of the numerator and denominator separately
3k23y2
Multiply by the Conjugate
3k2×3k3y2×3k
Calculate
k3y2×3k
The product of roots with the same index is equal to the root of the product
k3y2k
Calculate
k3ky2
x=k3ky2
Show Solution