Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to m
Find the first partial derivative with respect to h
∂m∂q=h−h2
Evaluate
q=m(h×1−h2)
Any expression multiplied by 1 remains the same
q=m(h−h2)
Find the first partial derivative by treating the variable h as a constant and differentiating with respect to m
∂m∂q=∂m∂(m(h−h2))
Use differentiation rule ∂x∂(f(x)×g(x))=∂x∂(f(x))×g(x)+f(x)×∂x∂(g(x))
∂m∂q=∂m∂(m)(h−h2)+m×∂m∂(h−h2)
Use ∂x∂xn=nxn−1 to find derivative
∂m∂q=1×(h−h2)+m×∂m∂(h−h2)
Evaluate
∂m∂q=h−h2+m×∂m∂(h−h2)
Use ∂x∂(c)=0 to find derivative
∂m∂q=h−h2+m×0
Evaluate
∂m∂q=h−h2+0
Solution
∂m∂q=h−h2
Show Solution
Solve the equation
Solve for h
Solve for m
Solve for q
h=2mm−m2−4mqh=2mm+m2−4mq
Evaluate
q=m(h×1−h2)
Any expression multiplied by 1 remains the same
q=m(h−h2)
Swap the sides of the equation
m(h−h2)=q
Divide both sides
mm(h−h2)=mq
Divide the numbers
h−h2=mq
Move the expression to the left side
h−h2−mq=0
Multiply both sides of the equation by LCD
(h−h2−mq)m=0×m
Simplify the equation
More Steps
Evaluate
(h−h2−mq)m
Apply the distributive property
hm−h2m−mq×m
Simplify
hm−h2m−q
Multiply the terms
mh−h2m−q
Multiply the terms
mh−mh2−q
mh−mh2−q=0×m
Any expression multiplied by 0 equals 0
mh−mh2−q=0
Rewrite in standard form
−mh2+mh−q=0
Substitute a=−m,b=m and c=−q into the quadratic formula h=2a−b±b2−4ac
h=2(−m)−m±m2−4(−m)(−q)
Simplify the expression
h=−2m−m±m2−4(−m)(−q)
Simplify the expression
More Steps
Evaluate
m2−4(−m)(−q)
Multiply the terms
More Steps
Evaluate
4(−m)(−q)
Use the commutative property to reorder the terms
−4m(−q)
Rewrite the expression
4mq
m2−4mq
h=−2m−m±m2−4mq
Separate the equation into 2 possible cases
h=−2m−m+m2−4mqh=−2m−m−m2−4mq
Simplify the expression
More Steps
Evaluate
h=−2m−m+m2−4mq
Divide the terms
More Steps
Evaluate
−2m−m+m2−4mq
Use b−a=−ba=−ba to rewrite the fraction
−2m−m+m2−4mq
Rewrite the expression
2mm−m2−4mq
h=2mm−m2−4mq
h=2mm−m2−4mqh=−2m−m−m2−4mq
Solution
h=2mm−m2−4mqh=2mm+m2−4mq
Show Solution