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

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

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expand (x^2+1)(d^2y)/(dx^2)

expand

(x^{2} + 1) \frac{d ^{2} y}{d x ^{2}}

x^{2} \frac{d ^{2} y}{d x ^{2}} + \frac{d ^{2} y}{d x ^{2}}

Solution steps

(x^{2} + 1) \frac{d ^{2} y}{d x ^{2}}

Apply the distributive law:

a (b + c) = ab + a c

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

= \frac{d ^{2} y}{d x ^{2}} x^{2} + \frac{d ^{2} y}{d x ^{2}} 1

= x^{2} \frac{d ^{2} y}{d x ^{2}} + 1 \frac{d ^{2} y}{d x ^{2}}

Multiply:

1 \frac{d ^{2} y}{d x ^{2}} = \frac{d ^{2} y}{d x ^{2}}

= x^{2} \frac{d ^{2} y}{d x ^{2}} + \frac{d ^{2} y}{d x ^{2}}

\frac{x ( 16 - x ) ^{2}}{2}

\frac{16}{15000} - 4.9908 (\frac{1}{15000} + \frac{1}{6800})

5 (4 - 7)

\frac{( 2 - 3 i ) ^{4} ( 1 - i ) ^{3}}{( 5 + i )}

- (2 - \frac{3}{m})^{2}

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