Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to x
Find the first partial derivative with respect to m
∂x∂y=18x2m
Evaluate
y=2x2×3xm
Multiply
More Steps
Evaluate
2x2×3xm
Multiply the terms
6x2×xm
Multiply the terms with the same base by adding their exponents
6x2+1m
Add the numbers
6x3m
y=6x3m
Find the first partial derivative by treating the variable m as a constant and differentiating with respect to x
∂x∂y=∂x∂(6x3m)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂x∂y=6m×∂x∂(x3)
Use ∂x∂xn=nxn−1 to find derivative
∂x∂y=6m×3x2
Solution
∂x∂y=18x2m
Show Solution
Solve the equation
Solve for x
Solve for m
Solve for y
x=6m336ym2
Evaluate
y=2x2×3xm
Multiply
More Steps
Evaluate
2x2×3xm
Multiply the terms
6x2×xm
Multiply the terms with the same base by adding their exponents
6x2+1m
Add the numbers
6x3m
y=6x3m
Rewrite the expression
y=6mx3
Swap the sides of the equation
6mx3=y
Divide both sides
6m6mx3=6my
Divide the numbers
x3=6my
Take the 3-th root on both sides of the equation
3x3=36my
Calculate
x=36my
Simplify the root
More Steps
Evaluate
36my
To take a root of a fraction,take the root of the numerator and denominator separately
36m3y
Multiply by the Conjugate
36m×362m23y×362m2
Calculate
6m3y×362m2
Calculate
More Steps
Evaluate
3y×362m2
The product of roots with the same index is equal to the root of the product
3y×62m2
Calculate the product
362ym2
6m362ym2
x=6m362ym2
Solution
More Steps
Evaluate
362ym2
Rewrite the expression
362×3y×3m2
Simplify the root
336ym2
x=6m336ym2
Show Solution