Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to x
Find the first partial derivative with respect to a
∂x∂y=−12x2a
Simplify
y=−4x3a
Find the first partial derivative by treating the variable a as a constant and differentiating with respect to x
∂x∂y=∂x∂(−4x3a)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂x∂y=−4a×∂x∂(x3)
Use ∂x∂xn=nxn−1 to find derivative
∂x∂y=−4a×3x2
Solution
∂x∂y=−12x2a
Show Solution
Solve the equation
Solve for x
Solve for a
x=−2a32ya2
Evaluate
y=−4x3a
Rewrite the expression
y=−4ax3
Swap the sides of the equation
−4ax3=y
Divide both sides
−4a−4ax3=−4ay
Divide the numbers
x3=−4ay
Use b−a=−ba=−ba to rewrite the fraction
x3=−4ay
Take the 3-th root on both sides of the equation
3x3=3−4ay
Calculate
x=3−4ay
Simplify the root
More Steps
Evaluate
3−4ay
To take a root of a fraction,take the root of the numerator and denominator separately
34a3−y
Multiply by the Conjugate
34a×342a23−y×342a2
Calculate
22a3−y×342a2
Calculate
More Steps
Evaluate
3−y×342a2
The product of roots with the same index is equal to the root of the product
3−y×42a2
Calculate the product
3−42ya2
22a3−42ya2
Calculate
4a3−42ya2
x=4a3−42ya2
Solution
More Steps
Evaluate
4a3−42ya2
Rewrite the expression
More Steps
Evaluate
3−42ya2
Rewrite the expression
3−42×3y×3a2
Simplify the root
−232ya2
−4a232ya2
Reduce the fraction
−2a32ya2
x=−2a32ya2
Show Solution