Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to a
Find the first partial derivative with respect to b
∂a∂u=2ab
Simplify
u=a2b
Find the first partial derivative by treating the variable b as a constant and differentiating with respect to a
∂a∂u=∂a∂(a2b)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂a∂u=b×∂a∂(a2)
Use ∂x∂xn=nxn−1 to find derivative
∂a∂u=b×2a
Solution
∂a∂u=2ab
Show Solution
Solve the equation
Solve for a
Solve for b
a=∣b∣bua=−∣b∣bu
Evaluate
u=a2b
Rewrite the expression
u=ba2
Swap the sides of the equation
ba2=u
Divide both sides
bba2=bu
Divide the numbers
a2=bu
Take the root of both sides of the equation and remember to use both positive and negative roots
a=±bu
Simplify the expression
More Steps
Evaluate
bu
Rewrite the expression
b×bub
Use the commutative property to reorder the terms
b×bbu
Calculate
b2bu
To take a root of a fraction,take the root of the numerator and denominator separately
b2bu
Simplify the radical expression
∣b∣bu
a=±∣b∣bu
Solution
a=∣b∣bua=−∣b∣bu
Show Solution