Answer to Question #283475 in Calculus for Ruchi

Question #283475

Find the second derivative of 3y^4+x^7=5x

Expert's answer

3y⁴+x⁷=5x

Differentiating with respect to x

12y³"\\frac{dy}{dx}+7x\u2076 = 5"

=> 12y³"\\frac{dy}{dx}" = 5 - 7x⁶

=> "\\frac{dy}{dx}" = "\\frac{5-7x\u2076}{12y\u00b3}" ••••••••(1)

Now 12y³"\\frac{dy}{dx}+7x\u2076 = 5"

Differentiating again with respect to x

"12y\u00b3\\frac{d\u00b2y}{dx\u00b2}+ 36y\u00b2{(\\frac{dy}{dx})}^2" + 42x⁵ = 0

=> "2y\u00b3\\frac{d\u00b2y}{dx\u00b2}+ 6y\u00b2{(\\frac{dy}{dx})}^2" + 7x⁵ = 0

"2y\u00b3\\frac{d\u00b2y}{dx\u00b2}+ 6y\u00b2{(\\frac{5-7x\u2076}{12y\u00b3})}^2+7x\u2075=0"

=> "2y\u00b3\\frac{d\u00b2y}{dx\u00b2}= -6y\u00b2{(\\frac{5-7x\u2076}{12y\u00b3})}^2-7x\u2075"

=> "\\frac{d\u00b2y}{dx\u00b2}= \\frac{ -6y\u00b2{(\\frac{5-7x\u2076}{12y\u00b3})}^2-7x\u2075}{2y\u00b3}"

=> "\\frac{d\u00b2y}{dx\u00b2}=- \\frac{ 6y\u00b2{(\\frac{5-7x\u2076}{12y\u00b3})}^2+7x\u2075}{2y\u00b3}"

=> "\\frac{d\u00b2y}{dx\u00b2}=- \\frac{ 6y\u00b2{(\\frac{(5-7x\u2076)\u00b2}{144y\u2076})}+7x\u2075}{2y\u00b3}"

=> "\\frac{d\u00b2y}{dx\u00b2}=- \\frac{ {(\\frac{(5-7x\u2076)\u00b2}{24y\u2074})}+7x\u2075}{2y\u00b3}"

=> "\\frac{d\u00b2y}{dx\u00b2}=- \\frac{ (5-7x\u2076)\u00b2+168x\u2075y\u2074}{48y\u2077}"

No comments. Be the first!