Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to x
Find the first partial derivative with respect to z
∂x∂a=3x2z
Simplify
a=x3z
Find the first partial derivative by treating the variable z as a constant and differentiating with respect to x
∂x∂a=∂x∂(x3z)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂x∂a=z×∂x∂(x3)
Use ∂x∂xn=nxn−1 to find derivative
∂x∂a=z×3x2
Solution
∂x∂a=3x2z
Show Solution
Solve the equation
Solve for x
Solve for z
x=z3az2
Evaluate
a=x3z
Rewrite the expression
a=zx3
Swap the sides of the equation
zx3=a
Divide both sides
zzx3=za
Divide the numbers
x3=za
Take the 3-th root on both sides of the equation
3x3=3za
Calculate
x=3za
Solution
More Steps
Evaluate
3za
To take a root of a fraction,take the root of the numerator and denominator separately
3z3a
Multiply by the Conjugate
3z×3z23a×3z2
Calculate
z3a×3z2
The product of roots with the same index is equal to the root of the product
z3az2
x=z3az2
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