Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to s
Find the first partial derivative with respect to t
∂s∂x=2st
Simplify
x=s2t
Find the first partial derivative by treating the variable t as a constant and differentiating with respect to s
∂s∂x=∂s∂(s2t)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂s∂x=t×∂s∂(s2)
Use ∂x∂xn=nxn−1 to find derivative
∂s∂x=t×2s
Solution
∂s∂x=2st
Show Solution
Solve the equation
Solve for s
Solve for t
s=∣t∣txs=−∣t∣tx
Evaluate
x=s2t
Rewrite the expression
x=ts2
Swap the sides of the equation
ts2=x
Divide both sides
tts2=tx
Divide the numbers
s2=tx
Take the root of both sides of the equation and remember to use both positive and negative roots
s=±tx
Simplify the expression
More Steps
Evaluate
tx
Rewrite the expression
t×txt
Use the commutative property to reorder the terms
t×ttx
Calculate
t2tx
To take a root of a fraction,take the root of the numerator and denominator separately
t2tx
Simplify the radical expression
∣t∣tx
s=±∣t∣tx
Solution
s=∣t∣txs=−∣t∣tx
Show Solution