Question
Function
Find the first partial derivative with respect to r
Find the first partial derivative with respect to f
∂r∂x=sin(f)
Simplify
x=rsin(f)
Find the first partial derivative by treating the variable f as a constant and differentiating with respect to r
∂r∂x=∂r∂(rsin(f))
Use differentiation rule ∂x∂(f(x)×g(x))=∂x∂(f(x))×g(x)+f(x)×∂x∂(g(x))
∂r∂x=∂r∂(r)sin(f)+r×∂r∂(sin(f))
Use ∂x∂xn=nxn−1 to find derivative
∂r∂x=1×sin(f)+r×∂r∂(sin(f))
Evaluate
∂r∂x=sin(f)+r×∂r∂(sin(f))
Use ∂x∂(c)=0 to find derivative
∂r∂x=sin(f)+r×0
Evaluate
∂r∂x=sin(f)+0
Solution
∂r∂x=sin(f)
Show Solution

Solve the equation
Solve for f
Solve for r
f=arcsin(rx)
Evaluate
x=rsin(f)
Swap the sides of the equation
rsin(f)=x
Multiply both sides of the equation by r1
rsin(f)×r1=x×r1
Calculate
sin(f)=x×r1
Calculate the product
sin(f)=rx
Solution
f=arcsin(rx)
Show Solution
