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Popular >

derivative of 2x+2y(dy/(dx))

Solution

\frac{d}{d x} (2 x + 2 y \frac{d y}{d x})

Solution

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

Solution steps

\frac{d}{d x} (2 x + 2 y \frac{d y}{d x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (2 x) = 2

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

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

Popular Examples

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y = 2 x, y = \frac{( x ^{2} )}{4}

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\int 5 x^{4} e^{4 x^{5}} d x

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\frac{d y}{d x}, y = x^{4}

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Frequently Asked Questions (FAQ)

What is the derivative of 2x+2y(dy/(dx)) ?
The derivative of 2x+2y(dy/(dx)) is 2+2((dy)/(dx)^2+(d^2y)/(dx^2)y)
What is the first derivative of 2x+2y(dy/(dx)) ?
The first derivative of 2x+2y(dy/(dx)) is 2+2((dy)/(dx)^2+(d^2y)/(dx^2)y)