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

The answer to (d^2)/(dx^2)((y)(x^2)) is x^2(d^2y)/(dx^2)+4x(dy)/(dx)+2y

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(d^2)/(dx^2)((y)(x^2))

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

x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} + 2 y

Solution steps

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

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

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

\frac{d}{d x} (\frac{d y}{d x} x^{2} + 2 x y) = x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} + 2 y

= x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} + 2 y

sin^{6} (a) + cos^{6} (a)

(3 x) - 2

(x + y)^{2} + 4 (x + y) + 4

(x + Δ x)^{3} - x^{3}

2 (x cos (ln (x)))

What is (d^2)/(dx^2)((y)(x^2)) ?
The answer to (d^2)/(dx^2)((y)(x^2)) is x^2(d^2y)/(dx^2)+4x(dy)/(dx)+2y