What is expand (7x^2+1)*(d^2y)/(dx^2) ?

The solution to expand (7x^2+1)*(d^2y)/(dx^2) is 7x^2(d^2y)/(dx^2)+(d^2y)/(dx^2)

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expand (7x^2+1)*(d^2y)/(dx^2)

expand

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

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

Solution steps

(7 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 = 7 x^{2}, c = 1

= \frac{d ^{2} y}{d x ^{2}} 7 x^{2} + \frac{d ^{2} y}{d x ^{2}} 1

= 7 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}}

= 7 x^{2} \frac{d ^{2} y}{d x ^{2}} + \frac{d ^{2} y}{d x ^{2}}

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What is expand (7x^2+1)*(d^2y)/(dx^2) ?
The solution to expand (7x^2+1)*(d^2y)/(dx^2) is 7x^2(d^2y)/(dx^2)+(d^2y)/(dx^2)