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=18x2y
Simplify
z=6x3y
Find the first partial derivative by treating the variable y as a constant and differentiating with respect to x
∂x∂z=∂x∂(6x3y)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂x∂z=6y×∂x∂(x3)
Use ∂x∂xn=nxn−1 to find derivative
∂x∂z=6y×3x2
Solution
∂x∂z=18x2y
Show Solution
Solve the equation
Solve for x
Solve for y
x=6y336zy2
Evaluate
z=6x3y
Rewrite the expression
z=6yx3
Swap the sides of the equation
6yx3=z
Divide both sides
6y6yx3=6yz
Divide the numbers
x3=6yz
Take the 3-th root on both sides of the equation
3x3=36yz
Calculate
x=36yz
Simplify the root
More Steps
Evaluate
36yz
To take a root of a fraction,take the root of the numerator and denominator separately
36y3z
Multiply by the Conjugate
36y×362y23z×362y2
Calculate
6y3z×362y2
Calculate
More Steps
Evaluate
3z×362y2
The product of roots with the same index is equal to the root of the product
3z×62y2
Calculate the product
362zy2
6y362zy2
x=6y362zy2
Solution
More Steps
Evaluate
362zy2
Rewrite the expression
362×3z×3y2
Simplify the root
336zy2
x=6y336zy2
Show Solution