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=6x2y
Simplify
z=2x3y
Find the first partial derivative by treating the variable y as a constant and differentiating with respect to x
∂x∂z=∂x∂(2x3y)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂x∂z=2y×∂x∂(x3)
Use ∂x∂xn=nxn−1 to find derivative
∂x∂z=2y×3x2
Solution
∂x∂z=6x2y
Show Solution
Solve the equation
Solve for x
Solve for y
x=2y34zy2
Evaluate
z=2x3y
Rewrite the expression
z=2yx3
Swap the sides of the equation
2yx3=z
Divide both sides
2y2yx3=2yz
Divide the numbers
x3=2yz
Take the 3-th root on both sides of the equation
3x3=32yz
Calculate
x=32yz
Simplify the root
More Steps
Evaluate
32yz
To take a root of a fraction,take the root of the numerator and denominator separately
32y3z
Multiply by the Conjugate
32y×322y23z×322y2
Calculate
2y3z×322y2
Calculate
More Steps
Evaluate
3z×322y2
The product of roots with the same index is equal to the root of the product
3z×22y2
Calculate the product
322zy2
2y322zy2
x=2y322zy2
Solution
More Steps
Evaluate
322zy2
Rewrite the expression
322×3z×3y2
Simplify the root
34zy2
x=2y34zy2
Show Solution