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Popular >

(d^4)/(dx^4)((y)(2x^5-2x))

Solution

\frac{d ^{4}}{d x ^{4}} ((y) (2 x^{5} - 2 x))

Solution

2 x^{5} \frac{d ^{4} y}{d x ^{4}} + 40 x^{4} \frac{d ^{3} y}{d x ^{3}} + 240 x^{3} \frac{d ^{2} y}{d x ^{2}} + 480 x^{2} \frac{d y}{d x} + 240 x y - 2 x \frac{d ^{4} y}{d x ^{4}} - 2 \frac{d ^{3} y}{d x ^{3}} - 6 \frac{d}{d x} (\frac{d ^{2} y}{d x ^{2}})

Solution steps

\frac{d ^{4}}{d x ^{4}} ((y) (2 x^{5} - 2 x))

\frac{d}{d x} (y (2 x^{5} - 2 x)) = \frac{d y}{d x} (2 x^{5} - 2 x) + (10 x^{4} - 2) y

= \frac{d ^{3}}{d x ^{3}} (\frac{d y}{d x} (2 x^{5} - 2 x) + (10 x^{4} - 2) y)

\frac{d}{d x} (\frac{d y}{d x} (2 x^{5} - 2 x) + (10 x^{4} - 2) y) = \frac{d ^{2} y}{d x ^{2}} (2 x^{5} - 2 x) + 2 \frac{d y}{d x} (10 x^{4} - 2) + 40 x^{3} y

= \frac{d ^{2}}{d x ^{2}} (\frac{d ^{2} y}{d x ^{2}} (2 x^{5} - 2 x) + 2 \frac{d y}{d x} (10 x^{4} - 2) + 40 x^{3} y)

\frac{d}{d x} (\frac{d ^{2} y}{d x ^{2}} (2 x^{5} - 2 x) + 2 \frac{d y}{d x} (10 x^{4} - 2) + 40 x^{3} y) = 2 x^{5} \frac{d ^{3} y}{d x ^{3}} + 30 x^{4} \frac{d ^{2} y}{d x ^{2}} + 120 x^{3} \frac{d y}{d x} + 120 x^{2} y - 2 x \frac{d ^{3} y}{d x ^{3}} - 6 \frac{d ^{2} y}{d x ^{2}}

= \frac{d}{d x} (2 x^{5} \frac{d ^{3} y}{d x ^{3}} + 30 x^{4} \frac{d ^{2} y}{d x ^{2}} + 120 x^{3} \frac{d y}{d x} + 120 x^{2} y - 2 x \frac{d ^{3} y}{d x ^{3}} - 6 \frac{d ^{2} y}{d x ^{2}})

\frac{d}{d x} (2 x^{5} \frac{d ^{3} y}{d x ^{3}} + 30 x^{4} \frac{d ^{2} y}{d x ^{2}} + 120 x^{3} \frac{d y}{d x} + 120 x^{2} y - 2 x \frac{d ^{3} y}{d x ^{3}} - 6 \frac{d ^{2} y}{d x ^{2}}) = 2 x^{5} \frac{d ^{4} y}{d x ^{4}} + 40 x^{4} \frac{d ^{3} y}{d x ^{3}} + 240 x^{3} \frac{d ^{2} y}{d x ^{2}} + 480 x^{2} \frac{d y}{d x} + 240 x y - 2 x \frac{d ^{4} y}{d x ^{4}} - 2 \frac{d ^{3} y}{d x ^{3}} - 6 \frac{d}{d x} (\frac{d ^{2} y}{d x ^{2}})

= 2 x^{5} \frac{d ^{4} y}{d x ^{4}} + 40 x^{4} \frac{d ^{3} y}{d x ^{3}} + 240 x^{3} \frac{d ^{2} y}{d x ^{2}} + 480 x^{2} \frac{d y}{d x} + 240 x y - 2 x \frac{d ^{4} y}{d x ^{4}} - 2 \frac{d ^{3} y}{d x ^{3}} - 6 \frac{d}{d x} (\frac{d ^{2} y}{d x ^{2}})

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Frequently Asked Questions (FAQ)

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