What is (\partial)/(\partial x)(t^2+4x^3) ?

The answer to (\partial)/(\partial x)(t^2+4x^3) is 12x^2

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(\partial)/(\partial x)(t^2+4x^3)

\frac{\partial}{\partial x} (t^{2} + 4 x^{3})

12 x^{2}

Solution steps

\frac{\partial}{\partial x} (t^{2} + 4 x^{3})

Treat

t

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (t^{2}) + \frac{\partial}{\partial x} (4 x^{3})

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

\frac{\partial}{\partial x} (4 x^{3}) = 12 x^{2}

= 0 + 12 x^{2}

Simplify

= 12 x^{2}

\int - \frac{1}{3} cos (3 x) d x

\int \frac{2 x ^{2}}{3 - 4 x ^{3}} d x

- 2

\frac{d}{d x} (arctan (x y))

\int \frac{( 3 x - 2 )}{5 x ^{2} - 3 x + 2} d x

What is (\partial)/(\partial x)(t^2+4x^3) ?
The answer to (\partial)/(\partial x)(t^2+4x^3) is 12x^2