Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to a
Find the first partial derivative with respect to t
∂a∂r=2at
Simplify
r=a2t
Find the first partial derivative by treating the variable t as a constant and differentiating with respect to a
∂a∂r=∂a∂(a2t)
Use differentiation rule ∂x∂(cf(x))=c×∂x∂(f(x))
∂a∂r=t×∂a∂(a2)
Use ∂x∂xn=nxn−1 to find derivative
∂a∂r=t×2a
Solution
∂a∂r=2at
Show Solution
Solve the equation
Solve for a
Solve for t
a=∣t∣rta=−∣t∣rt
Evaluate
r=a2t
Rewrite the expression
r=ta2
Swap the sides of the equation
ta2=r
Divide both sides
tta2=tr
Divide the numbers
a2=tr
Take the root of both sides of the equation and remember to use both positive and negative roots
a=±tr
Simplify the expression
More Steps
Evaluate
tr
Rewrite the expression
t×trt
Calculate
t2rt
To take a root of a fraction,take the root of the numerator and denominator separately
t2rt
Simplify the radical expression
∣t∣rt
a=±∣t∣rt
Solution
a=∣t∣rta=−∣t∣rt
Show Solution