Question
Function
Find the first partial derivative with respect to x
Find the first partial derivative with respect to c
∂x∂y=sin(c)
Evaluate
y=sin(c)×x
Multiply the terms
y=xsin(c)
Find the first partial derivative by treating the variable c as a constant and differentiating with respect to x
∂x∂y=∂x∂(xsin(c))
Use differentiation rule ∂x∂(f(x)×g(x))=∂x∂(f(x))×g(x)+f(x)×∂x∂(g(x))
∂x∂y=∂x∂(x)sin(c)+x×∂x∂(sin(c))
Use ∂x∂xn=nxn−1 to find derivative
∂x∂y=1×sin(c)+x×∂x∂(sin(c))
Evaluate
∂x∂y=sin(c)+x×∂x∂(sin(c))
Use ∂x∂(c)=0 to find derivative
∂x∂y=sin(c)+x×0
Evaluate
∂x∂y=sin(c)+0
Solution
∂x∂y=sin(c)
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Solve the equation
Solve for x
Solve for c
Solve for y
x=sin(c)y
Evaluate
y=sin(c)×x
Swap the sides of the equation
sin(c)×x=y
Divide both sides
sin(c)sin(c)×x=sin(c)y
Solution
x=sin(c)y
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