What is expand ((d^2x)/(dx^2))(1-x^2) ?

The solution to expand ((d^2x)/(dx^2))(1-x^2) is (d^2x)/(dx^2)-x^2(d^2x)/(dx^2)

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expand ((d^2x)/(dx^2))(1-x^2)

expand

(\frac{d ^{2} x}{d x ^{2}}) (1 - x^{2})

\frac{d ^{2} x}{d x ^{2}} - x^{2} \frac{d ^{2} x}{d x ^{2}}

Solution steps

(\frac{d ^{2} x}{d x ^{2}}) (1 - x^{2})

Apply the distributive law:

a (b - c) = ab - a c

a = (\frac{d ^{2} x}{d x ^{2}}), b = 1, c = x^{2}

= (\frac{d ^{2} x}{d x ^{2}}) \cdot 1 - (\frac{d ^{2} x}{d x ^{2}}) x^{2}

= 1 \cdot (\frac{d ^{2} x}{d x ^{2}}) - x^{2} (\frac{d ^{2} x}{d x ^{2}})

Simplify

1 \cdot (\frac{d ^{2} x}{d x ^{2}}) - x^{2} (\frac{d ^{2} x}{d x ^{2}}) : \frac{d ^{2} x}{d x ^{2}} - x^{2} \frac{d ^{2} x}{d x ^{2}}

= \frac{d ^{2} x}{d x ^{2}} - x^{2} \frac{d ^{2} x}{d x ^{2}}

e^{7 t} (27 \cdot U (t - 18))

\frac{( X ^{3} + X ^{2} + 5 X + 4 )}{( X ^{2} + 4 ) ^{2}}

x^{3} (x ln (x) - x)

(3 x y^{2} - 4 y) + (3 x - 4 x^{2} y) \cdot \frac{d y}{d x}

What is expand ((d^2x)/(dx^2))(1-x^2) ?
The solution to expand ((d^2x)/(dx^2))(1-x^2) is (d^2x)/(dx^2)-x^2(d^2x)/(dx^2)