Solve d=(v1-v^2)t

Evaluate

d = (v \times 1 - v^{2}) t

Simplify

More Steps

d = t (v - v^{2})

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

\frac{\partial d}{\partial t} = \frac{\partial}{\partial t} (t (v - v^{2}))

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 d}{\partial t} = \frac{\partial}{\partial t} (t) (v - v^{2}) + t \times \frac{\partial}{\partial t} (v - v^{2})

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

\frac{\partial d}{\partial t} = 1 \times (v - v^{2}) + t \times \frac{\partial}{\partial t} (v - v^{2})

Evaluate

\frac{\partial d}{\partial t} = v - v^{2} + t \times \frac{\partial}{\partial t} (v - v^{2})

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

\frac{\partial d}{\partial t} = v - v^{2} + t \times 0

Evaluate

\frac{\partial d}{\partial t} = v - v^{2} + 0

Solution

\frac{\partial d}{\partial t} = v - v^{2}

Function