What is (d^2)/(dx^2)((z)(x^2+y^2+z^2-c^2)) ?

The answer to (d^2)/(dx^2)((z)(x^2+y^2+z^2-c^2)) is

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(d^2)/(dx^2)((z)(x^2+y^2+z^2-c^2))

\frac{d ^{2}}{d x ^{2}} ((z) (x^{2} + y^{2} + z^{2} - c^{2}))

x^{2} \frac{d ^{2} z}{d x ^{2}} + 4 x \frac{d z}{d x} - c^{2} \frac{d ^{2} z}{d x ^{2}} + 2 z + 4 y \frac{d z}{d x} \frac{d y}{d x} + y^{2} \frac{d ^{2} z}{d x ^{2}} + 6 z \frac{d z}{d x}^{2} + 3 z^{2} \frac{d ^{2} z}{d x ^{2}} + 2 z \frac{d y}{d x}^{2} + 2 zy (x) \frac{d ^{2} y}{d x ^{2}}

Solution steps

\frac{d ^{2}}{d x ^{2}} ((z) (x^{2} + y^{2} + z^{2} - c^{2}))

\frac{d}{d x} (z (x^{2} + y^{2} + z^{2} - c^{2})) = x^{2} \frac{d z}{d x} + 2 x z - c^{2} \frac{d z}{d x} + y^{2} \frac{d z}{d x} + 3 z^{2} \frac{d z}{d x} + 2 zy (x) \frac{d y}{d x}

= \frac{d}{d x} (x^{2} \frac{d z}{d x} + 2 x z - c^{2} \frac{d z}{d x} + y^{2} \frac{d z}{d x} + 3 z^{2} \frac{d z}{d x} + 2 zy (x) \frac{d y}{d x})

\frac{d}{d x} (x^{2} \frac{d z}{d x} + 2 x z - c^{2} \frac{d z}{d x} + y^{2} \frac{d z}{d x} + 3 z^{2} \frac{d z}{d x} + 2 zy (x) \frac{d y}{d x}) = x^{2} \frac{d ^{2} z}{d x ^{2}} + 4 x \frac{d z}{d x} - c^{2} \frac{d ^{2} z}{d x ^{2}} + 2 z + 4 y \frac{d z}{d x} \frac{d y}{d x} + y^{2} \frac{d ^{2} z}{d x ^{2}} + 6 z \frac{d z}{d x}^{2} + 3 z^{2} \frac{d ^{2} z}{d x ^{2}} + 2 z \frac{d y}{d x}^{2} + 2 zy (x) \frac{d ^{2} y}{d x ^{2}}

= x^{2} \frac{d ^{2} z}{d x ^{2}} + 4 x \frac{d z}{d x} - c^{2} \frac{d ^{2} z}{d x ^{2}} + 2 z + 4 y \frac{d z}{d x} \frac{d y}{d x} + y^{2} \frac{d ^{2} z}{d x ^{2}} + 6 z \frac{d z}{d x}^{2} + 3 z^{2} \frac{d ^{2} z}{d x ^{2}} + 2 z \frac{d y}{d x}^{2} + 2 zy (x) \frac{d ^{2} y}{d x ^{2}}

\frac{10 - 4 s ^{2} - 11 s}{s ( s ^{2} - 2 s + 1 )}

\frac{( 2 - x ) ( ln ( 1 - x ) )}{x}

e^{y} (\frac{d y}{d x} + 1) =!

\frac{( x - 2 ) ( 2 x + 3 )}{x + 47}

5 - 3 \cdot 2

What is (d^2)/(dx^2)((z)(x^2+y^2+z^2-c^2)) ?
The answer to (d^2)/(dx^2)((z)(x^2+y^2+z^2-c^2)) is