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Popular >

(d^2)/(dx^2)(4sqrt(y^2+7x^2))

Solution

\frac{d ^{2}}{d x ^{2}} (4 y^{2} + 7 x^{2})

Solution

\frac{2 ( 14 x ^{2} \frac{d y}{d x} ^{2} + 14 x ^{2} y \frac{d ^{2} y}{d x ^{2}} - 28 x y \frac{d y}{d x} + 14 y ^{2} + 2 y ^{3} \frac{d ^{2} y}{d x ^{2}} )}{( y ^{2} + 7 x ^{2} ) y ^{2} + 7 x ^{2}}

Solution steps

\frac{d ^{2}}{d x ^{2}} (4 y^{2} + 7 x^{2})

\frac{d}{d x} (4 y^{2} + 7 x^{2}) = \frac{2 ( 14 x + 2 y \frac{d y}{d x} )}{y ^{2} + 7 x ^{2}}

= \frac{d}{d x} \frac{2 ( 14 x + 2 y \frac{d y}{d x} )}{y ^{2} + 7 x ^{2}}

\frac{d}{d x} \frac{2 ( 14 x + 2 y \frac{d y}{d x} )}{y ^{2} + 7 x ^{2}} = \frac{2 ( 14 x ^{2} \frac{d y}{d x} ^{2} + 14 x ^{2} y \frac{d ^{2} y}{d x ^{2}} - 28 x y \frac{d y}{d x} + 14 y ^{2} + 2 y ^{3} \frac{d ^{2} y}{d x ^{2}} )}{( y ^{2} + 7 x ^{2} ) y ^{2} + 7 x ^{2}}

= \frac{2 ( 14 x ^{2} \frac{d y}{d x} ^{2} + 14 x ^{2} y \frac{d ^{2} y}{d x ^{2}} - 28 x y \frac{d y}{d x} + 14 y ^{2} + 2 y ^{3} \frac{d ^{2} y}{d x ^{2}} )}{( y ^{2} + 7 x ^{2} ) y ^{2} + 7 x ^{2}}

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\int 10 sec (2 x) tan (2 x) d x

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\int cosh (x) sinh (x) d x

Frequently Asked Questions (FAQ)

What is (d^2)/(dx^2)(4sqrt(y^2+7x^2)) ?
The answer to (d^2)/(dx^2)(4sqrt(y^2+7x^2)) is