(d^2)/(dx^2)((y)(x^2+y^2-25))

解答

\frac{d ^{2}}{d x ^{2}} ((y) (x^{2} + y^{2} - 25))

x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} + 2 y + 6 y \frac{d y}{d x}^{2} + 3 y^{2} \frac{d ^{2} y}{d x ^{2}} - 25 \frac{d}{d x} (\frac{d y}{d x})

求解步骤

\frac{d ^{2}}{d x ^{2}} ((y) (x^{2} + y^{2} - 25))

\frac{d}{d x} (y (x^{2} + y^{2} - 25)) = x^{2} \frac{d y}{d x} + 2 x y + 3 y^{2} \frac{d y}{d x} - 25 \frac{d y}{d x}

= \frac{d}{d x} (x^{2} \frac{d y}{d x} + 2 x y + 3 y^{2} \frac{d y}{d x} - 25 \frac{d y}{d x})

\frac{d}{d x} (x^{2} \frac{d y}{d x} + 2 x y + 3 y^{2} \frac{d y}{d x} - 25 \frac{d y}{d x}) = x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} + 2 y + 6 y \frac{d y}{d x}^{2} + 3 y^{2} \frac{d ^{2} y}{d x ^{2}} - 25 \frac{d}{d x} (\frac{d y}{d x})

= x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} + 2 y + 6 y \frac{d y}{d x}^{2} + 3 y^{2} \frac{d ^{2} y}{d x ^{2}} - 25 \frac{d}{d x} (\frac{d y}{d x})

e x p an d (tan (x) + sec (x)) (1 - sin (x))

e x p an d \frac{( x ^{4} )}{( x - 1 ) ^{3}}

e x p an d cos (2 t) μ (t - π)

e x p an d \frac{( 4 y + 1 ) ^{2}}{16}

s im pl i f y (x + 33) (x - 33)