Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to q
Find the first partial derivative with respect to l
∂q∂m=81l2
Evaluate
m=q×8l2
Multiply the terms
m=8ql2
Find the first partial derivative by treating the variable l as a constant and differentiating with respect to q
∂q∂m=∂q∂(8ql2)
Use differentiation rules
∂q∂m=81×∂q∂(ql2)
Solution
More Steps
Evaluate
∂q∂(ql2)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
l2×∂q∂(q)
Use ∂x∂xn=nxn−1 to find derivative
l2×1
Multiply the terms
l2
∂q∂m=81l2
Show Solution
Solve the equation
Solve for l
Solve for m
Solve for q
l=∣q∣22qml=−∣q∣22qm
Evaluate
m=q×8l2
Multiply the terms
m=8ql2
Swap the sides of the equation
8ql2=m
Cross multiply
ql2=8m
Divide both sides
qql2=q8m
Divide the numbers
l2=q8m
Take the root of both sides of the equation and remember to use both positive and negative roots
l=±q8m
Simplify the expression
More Steps
Evaluate
q8m
Rewrite the expression
q×q8mq
Calculate
q28mq
To take a root of a fraction,take the root of the numerator and denominator separately
q28mq
Simplify the radical expression
∣q∣8mq
l=±∣q∣8mq
Separate the equation into 2 possible cases
l=∣q∣8mql=−∣q∣8mq
Simplify
l=∣q∣22qml=−∣q∣8mq
Solution
l=∣q∣22qml=−∣q∣22qm
Show Solution