Question
Function
Find the first partial derivative with respect to t
Find the first partial derivative with respect to m
∂t∂x=3−6tm
Simplify
x=3t−3t2m
Find the first partial derivative by treating the variable m as a constant and differentiating with respect to t
∂t∂x=∂t∂(3t−3t2m)
Use differentiation rule ∂x∂(f(x)±g(x))=∂x∂(f(x))±∂x∂(g(x))
∂t∂x=∂t∂(3t)−∂t∂(3t2m)
Evaluate
More Steps

Evaluate
∂t∂(3t)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
3×∂t∂(t)
Use ∂x∂xn=nxn−1 to find derivative
3×1
Multiply the terms
3
∂t∂x=3−∂t∂(3t2m)
Solution
More Steps

Evaluate
∂t∂(3t2m)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
3m×∂t∂(t2)
Use ∂x∂xn=nxn−1 to find derivative
3m×2t
Multiply the terms
6tm
∂t∂x=3−6tm
Show Solution

Solve the equation
Solve for m
Solve for t
m=3t2−x+3t
Evaluate
x=3t−3t2m
Swap the sides of the equation
3t−3t2m=x
Move the expression to the right-hand side and change its sign
−3t2m=x−3t
Divide both sides
−3t2−3t2m=−3t2x−3t
Divide the numbers
m=−3t2x−3t
Solution
More Steps

Evaluate
−3t2x−3t
Use b−a=−ba=−ba to rewrite the fraction
−3t2x−3t
Rewrite the expression
3t2−x+3t
m=3t2−x+3t
Show Solution
