What is (\partial)/(\partial t)((x)(x^3+xt+3t^3)) ?

The answer to (\partial)/(\partial t)((x)(x^3+xt+3t^3)) is x(x+9t^2)

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(\partial)/(\partial t)((x)(x^3+xt+3t^3))

\frac{\partial}{\partial t} ((x) (x^{3} + x t + 3 t^{3}))

x (x + 9 t^{2})

Solution steps

\frac{\partial}{\partial t} ((x) (x^{3} + x t + 3 t^{3}))

Treat

x

as a constant

Take the constant out:

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

= x \frac{\partial}{\partial t} (x^{3} + x t + 3 t^{3})

Apply the Sum/Difference Rule:

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

= x (\frac{\partial}{\partial t} (x^{3}) + \frac{\partial}{\partial t} (x t) + \frac{\partial}{\partial t} (3 t^{3}))

\frac{\partial}{\partial t} (x^{3}) = 0

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

\frac{\partial}{\partial t} (3 t^{3}) = 9 t^{2}

= x (0 + x + 9 t^{2})

Simplify

= x (x + 9 t^{2})

50 (100 - e^{\frac{x}{2}})

\frac{1}{3 a ^{2} b ^{2} ( b + a )}

\frac{x ^{2} + 3 x}{( 3 x + 1 ) ^{2}}

((e^{1.1 x} - e^{- 1.1 x}))^{2}

e^{(4 x)} (4 x - 16)

What is (\partial)/(\partial t)((x)(x^3+xt+3t^3)) ?
The answer to (\partial)/(\partial t)((x)(x^3+xt+3t^3)) is x(x+9t^2)