Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to l
Find the first partial derivative with respect to w
∂l∂p=4lw
Simplify
p=2l2w
Find the first partial derivative by treating the variable w as a constant and differentiating with respect to l
∂l∂p=∂l∂(2l2w)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂l∂p=2w×∂l∂(l2)
Use ∂x∂xn=nxn−1 to find derivative
∂l∂p=2w×2l
Solution
∂l∂p=4lw
Show Solution
Solve the equation
Solve for l
Solve for w
l=2∣w∣2pwl=−2∣w∣2pw
Evaluate
p=2l2w
Rewrite the expression
p=2wl2
Swap the sides of the equation
2wl2=p
Divide both sides
2w2wl2=2wp
Divide the numbers
l2=2wp
Take the root of both sides of the equation and remember to use both positive and negative roots
l=±2wp
Simplify the expression
More Steps
Evaluate
2wp
Rewrite the expression
2w×2wp×2w
Use the commutative property to reorder the terms
2w×2w2pw
Calculate
4w22pw
To take a root of a fraction,take the root of the numerator and denominator separately
4w22pw
Simplify the radical expression
More Steps
Evaluate
4w2
Rewrite the expression
4×w2
Simplify the root
2∣w∣
2∣w∣2pw
l=±2∣w∣2pw
Solution
l=2∣w∣2pwl=−2∣w∣2pw
Show Solution