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Popular >

(d^2)/(dx^2)((y)(3x^2-2x+5)^4)

Solution

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

Solution

\frac{d ^{2} y}{d x ^{2}} (3 x^{2} - 2 x + 5)^{4} + 48 x (3 x^{2} - 2 x + 5)^{3} \frac{d y}{d x} - 16 (3 x^{2} - 2 x + 5)^{3} \frac{d y}{d x} + 12 (3 x^{2} - 2 x + 5)^{2} (6 x - 2)^{2} y + 24 (3 x^{2} - 2 x + 5)^{3} y

Solution steps

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

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

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

\frac{d}{d x} (\frac{d y}{d x} (3 x^{2} - 2 x + 5)^{4} + 4 (3 x^{2} - 2 x + 5)^{3} (6 x - 2) y) = \frac{d ^{2} y}{d x ^{2}} (3 x^{2} - 2 x + 5)^{4} + 48 x (3 x^{2} - 2 x + 5)^{3} \frac{d y}{d x} - 16 (3 x^{2} - 2 x + 5)^{3} \frac{d y}{d x} + 12 (3 x^{2} - 2 x + 5)^{2} (6 x - 2)^{2} y + 24 (3 x^{2} - 2 x + 5)^{3} y

= \frac{d ^{2} y}{d x ^{2}} (3 x^{2} - 2 x + 5)^{4} + 48 x (3 x^{2} - 2 x + 5)^{3} \frac{d y}{d x} - 16 (3 x^{2} - 2 x + 5)^{3} \frac{d y}{d x} + 12 (3 x^{2} - 2 x + 5)^{2} (6 x - 2)^{2} y + 24 (3 x^{2} - 2 x + 5)^{3} y

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Frequently Asked Questions (FAQ)

What is (d^2)/(dx^2)((y)(3x^2-2x+5)^4) ?
The answer to (d^2)/(dx^2)((y)(3x^2-2x+5)^4) is