Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to m
Find the first partial derivative with respect to s
∂m∂t=243m2s
Evaluate
t=27m3×3s
Multiply the terms
t=81m3s
Find the first partial derivative by treating the variable s as a constant and differentiating with respect to m
∂m∂t=∂m∂(81m3s)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂m∂t=81s×∂m∂(m3)
Use ∂x∂xn=nxn−1 to find derivative
∂m∂t=81s×3m2
Solution
∂m∂t=243m2s
Show Solution
Solve the equation
Solve for m
Solve for s
Solve for t
m=9s39ts2
Evaluate
t=27m3×3s
Multiply the terms
t=81m3s
Rewrite the expression
t=81sm3
Swap the sides of the equation
81sm3=t
Divide both sides
81s81sm3=81st
Divide the numbers
m3=81st
Take the 3-th root on both sides of the equation
3m3=381st
Calculate
m=381st
Simplify the root
More Steps
Evaluate
381st
To take a root of a fraction,take the root of the numerator and denominator separately
381s3t
Simplify the radical expression
More Steps
Evaluate
381s
Rewrite the expression
381×3s
Simplify the root
333s
333s3t
Multiply by the Conjugate
333s×332s23t×332s2
Calculate
3×3s3t×332s2
Calculate
More Steps
Evaluate
3t×332s2
The product of roots with the same index is equal to the root of the product
3t×32s2
Calculate the product
332ts2
3×3s332ts2
Calculate
9s332ts2
m=9s332ts2
Solution
More Steps
Evaluate
332ts2
Rewrite the expression
332×3t×3s2
Simplify the root
39ts2
m=9s39ts2
Show Solution