Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to x
Find the first partial derivative with respect to y
∂x∂z=10x4y
Simplify
z=2x5y
Find the first partial derivative by treating the variable y as a constant and differentiating with respect to x
∂x∂z=∂x∂(2x5y)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂x∂z=2y×∂x∂(x5)
Use ∂x∂xn=nxn−1 to find derivative
∂x∂z=2y×5x4
Solution
∂x∂z=10x4y
Show Solution
Solve the equation
Solve for x
Solve for y
x=2y516zy4
Evaluate
z=2x5y
Rewrite the expression
z=2yx5
Swap the sides of the equation
2yx5=z
Divide both sides
2y2yx5=2yz
Divide the numbers
x5=2yz
Take the 5-th root on both sides of the equation
5x5=52yz
Calculate
x=52yz
Simplify the root
More Steps
Evaluate
52yz
To take a root of a fraction,take the root of the numerator and denominator separately
52y5z
Multiply by the Conjugate
52y×524y45z×524y4
Calculate
2y5z×524y4
Calculate
More Steps
Evaluate
5z×524y4
The product of roots with the same index is equal to the root of the product
5z×24y4
Calculate the product
524zy4
2y524zy4
x=2y524zy4
Solution
More Steps
Evaluate
524zy4
Rewrite the expression
524×5z×5y4
Simplify the root
516zy4
x=2y516zy4
Show Solution