Solve y=f|x| - ScanMath

Simplify

y = f ∣ x ∣

Find the first partial derivative by treating the variable x as a constant and differentiating with respect to f

\frac{\partial y}{\partial f} = \frac{\partial}{\partial f} (f ∣ x ∣)

Use differentiation rule \frac{\partial}{\partial x} (f (x) \times g (x)) = \frac{\partial}{\partial x} (f (x)) \times g (x) + f (x) \times \frac{\partial}{\partial x} (g (x))

\frac{\partial y}{\partial f} = \frac{\partial}{\partial f} (f) ∣ x ∣ + f \times \frac{\partial}{\partial f} (∣ x ∣)

Use \frac{\partial}{\partial x} x^{n} = n x^{n - 1} to find derivative

\frac{\partial y}{\partial f} = 1 \times ∣ x ∣ + f \times \frac{\partial}{\partial f} (∣ x ∣)

Evaluate

\frac{\partial y}{\partial f} = ∣ x ∣ + f \times \frac{\partial}{\partial f} (∣ x ∣)

Use \frac{\partial}{\partial x} (c) = 0 to find derivative

\frac{\partial y}{\partial f} = ∣ x ∣ + f \times 0

Evaluate

\frac{\partial y}{\partial f} = ∣ x ∣ + 0

Solution

\frac{\partial y}{\partial f} = ∣ x ∣

Function