Question
Function
Find the first partial derivative with respect to m
Find the first partial derivative with respect to s
∂m∂g=s2m
Simplify
g=sm2
Find the first partial derivative by treating the variable s as a constant and differentiating with respect to m
∂m∂g=∂m∂(sm2)
Use differentiation rule ∂x∂(g(x)f(x))=(g(x))2∂x∂(f(x))×g(x)−f(x)×∂x∂(g(x))
∂m∂g=s2∂m∂(m2)s−m2×∂m∂(s)
Use ∂x∂xn=nxn−1 to find derivative
∂m∂g=s22ms−m2×∂m∂(s)
Use ∂x∂(c)=0 to find derivative
∂m∂g=s22ms−m2×0
Any expression multiplied by 0 equals 0
∂m∂g=s22ms−0
Removing 0 doesn't change the value,so remove it from the expression
∂m∂g=s22ms
Solution
More Steps
Evaluate
s22ms
Use the product rule aman=an−m to simplify the expression
s2−12m
Reduce the fraction
s2m
∂m∂g=s2m
Show Solution
Solve the equation
Solve for m
Solve for s
m=gsm=−gs
Evaluate
g=sm2
Swap the sides of the equation
sm2=g
Cross multiply
m2=sg
Simplify the equation
m2=gs
Take the root of both sides of the equation and remember to use both positive and negative roots
m=±gs
Solution
m=gsm=−gs
Show Solution