Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to u
Find the first partial derivative with respect to v
∂u∂y=5u4v
Simplify
y=u5v−1
Find the first partial derivative by treating the variable v as a constant and differentiating with respect to u
∂u∂y=∂u∂(u5v−1)
Use differentiation rule ∂x∂(f(x)±g(x))=∂x∂(f(x))±∂x∂(g(x))
∂u∂y=∂u∂(u5v)−∂u∂(1)
Evaluate
More Steps
Evaluate
∂u∂(u5v)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
v×∂u∂(u5)
Use ∂x∂xn=nxn−1 to find derivative
v×5u4
Multiply the terms
5u4v
∂u∂y=5u4v−∂u∂(1)
Use ∂x∂(c)=0 to find derivative
∂u∂y=5u4v−0
Solution
∂u∂y=5u4v
Show Solution
Solve the equation
Solve for u
Solve for v
u=v5v4y+v4
Evaluate
y=u5v−1
Rewrite the expression
y=vu5−1
Swap the sides of the equation
vu5−1=y
Move the constant to the right-hand side and change its sign
vu5=y+1
Divide both sides
vvu5=vy+1
Divide the numbers
u5=vy+1
Take the 5-th root on both sides of the equation
5u5=5vy+1
Calculate
u=5vy+1
Solution
More Steps
Evaluate
5vy+1
To take a root of a fraction,take the root of the numerator and denominator separately
5v5y+1
Multiply by the Conjugate
5v×5v45y+1×5v4
Calculate
v5y+1×5v4
Calculate
More Steps
Evaluate
5y+1×5v4
The product of roots with the same index is equal to the root of the product
5(y+1)v4
Calculate the product
5yv4+v4
v5yv4+v4
Calculate
v5v4y+v4
u=v5v4y+v4
Show Solution