What is (\partial)/(\partial t)((x)(x^2+xt+t^2-1)) ?

The answer to (\partial)/(\partial t)((x)(x^2+xt+t^2-1)) is x(x+2t)

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(\partial)/(\partial t)((x)(x^2+xt+t^2-1))

\frac{\partial}{\partial t} ((x) (x^{2} + x t + t^{2} - 1))

x (x + 2 t)

Solution steps

\frac{\partial}{\partial t} ((x) (x^{2} + x t + t^{2} - 1))

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= x \frac{\partial}{\partial t} (x^{2} + x t + t^{2} - 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= x (\frac{\partial}{\partial t} (x^{2}) + \frac{\partial}{\partial t} (x t) + \frac{\partial}{\partial t} (t^{2}) - \frac{\partial}{\partial t} (1))

\frac{\partial}{\partial t} (x^{2}) = 0

\frac{\partial}{\partial t} (x t) = x

\frac{\partial}{\partial t} (t^{2}) = 2 t

\frac{\partial}{\partial t} (1) = 0

= x (0 + x + 2 t - 0)

Simplify

= x (x + 2 t)

y^{2} d x + (x y - x^{3}) d y

(10 x + 3) 5 - 2 x^{2} - 9 x

(1 + cot (θ))^{2}

(1 - 3 sin (x))^{2}

(a + b t) e^{3 t} - \frac{2}{5} e^{- 2 t}

What is (\partial)/(\partial t)((x)(x^2+xt+t^2-1)) ?
The answer to (\partial)/(\partial t)((x)(x^2+xt+t^2-1)) is x(x+2t)