Solve w = c(h^2 - h1) - Socratic AI (ScanMath)

Evaluate

w = c (h^{2} - h \times 1)

Any expression multiplied by 1 remains the same

w = c (h^{2} - h)

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

\frac{\partial w}{\partial c} = \frac{\partial}{\partial c} (c (h^{2} - h))

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 w}{\partial c} = \frac{\partial}{\partial c} (c) (h^{2} - h) + c \times \frac{\partial}{\partial c} (h^{2} - h)

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

\frac{\partial w}{\partial c} = 1 \times (h^{2} - h) + c \times \frac{\partial}{\partial c} (h^{2} - h)

Evaluate

\frac{\partial w}{\partial c} = h^{2} - h + c \times \frac{\partial}{\partial c} (h^{2} - h)

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

\frac{\partial w}{\partial c} = h^{2} - h + c \times 0

Evaluate

\frac{\partial w}{\partial c} = h^{2} - h + 0

Solución

\frac{\partial w}{\partial c} = h^{2} - h

W = c(h^2 h1)