Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to m
Find the first partial derivative with respect to k
∂m∂b=−3k
Evaluate
b=2.897771955×10−3mk
Simplify
b=28.97771955−3mk
Evaluate
b=2,897771955×10−3mk
Multiply the numbers
b=28,97771955−3mk
Find the first partial derivative by treating the variable k as a constant and differentiating with respect to m
∂m∂b=∂m∂(28,97771955−3mk)
Use differentiation rule ∂x∂(f(x)±g(x))=∂x∂(f(x))±∂x∂(g(x))
∂m∂b=∂m∂(28,97771955)−∂m∂(3mk)
Use ∂x∂(c)=0 to find derivative
∂m∂b=0−∂m∂(3mk)
Evaluate
More Steps
Evaluate
∂m∂(3mk)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
3k×∂m∂(m)
Use ∂x∂xn=nxn−1 to find derivative
3k×1
Multiply the terms
3k
∂m∂b=0−3k
Solution
∂m∂b=−3k
Show Solution
Solve the equation
Solve for k
Solve for m
k=60000000m−20000000b+579554391
Evaluate
b=28.97771955−3mk
Swap the sides of the equation
28.97771955−3mk=b
Move the constant to the right-hand side and change its sign
−3mk=b−28.97771955
Divide both sides
−3m−3mk=−3mb−28.97771955
Divide the numbers
k=−3mb−28.97771955
Divide the numbers
More Steps
Evaluate
−3mb−28.97771955
Use b−a=−ba=−ba to rewrite the fraction
−3mb−28.97771955
Rewrite the expression
3m−b+28.97771955
k=3m−b+28.97771955
Solution
More Steps
Evaluate
3m−b+28.97771955
Convert the decimal into a fraction
More Steps
Evaluate
28.97771955
Convert the decimal into a fraction
1000000002897771955
Reduce the fraction
20000000579554391
3m−b+20000000579554391
Simplify the expression
60000000m−20000000b+579554391
k=60000000m−20000000b+579554391
Show Solution