What is (\partial)/(\partial x)(x^2(x-2)^4) ?

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

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(\partial)/(\partial x)(x^2(x-2)^4)

\frac{\partial}{\partial x} (x^{2} (x - 2)^{4})

2 x (x - 2)^{4} + 4 (x - 2)^{3} x^{2}

Solution steps

\frac{\partial}{\partial x} (x^{2} (x - 2)^{4})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = (x - 2)^{4}

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

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

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

= 2 x (x - 2)^{4} + 4 (x - 2)^{3} x^{2}

x^{2} y^{^{''}} + 3 x y^{^{'}} - 3 y = 0, y (1) = 0, y^{^{'}} (1) = 5

\int_{0}^{\frac{π}{4}} x sin (12 x) d x

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

y^{^{''}} - 4 y^{^{'}} - 5 y = - 2, y (0) = 0, y^{^{'}} (0) = 0

\frac{d}{d x} (e^{3 x} cos (x))

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