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Popular >

derivative of x(dy/(dx))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = \frac{d y}{d x}

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

\frac{d x}{d x} = 1

= 1 \frac{d y}{d x} + \frac{d ^{2} y}{d x ^{2}} x

Simplify

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

Popular Examples

y^'+3y=2e^{-3t}

y^{^{'}} + 3 y = 2 e^{- 3 t}

derivative of f(x)=((sqrt(x)-2))/((2x^2+3))derivative of

f (x) = \frac{( x - 2 )}{( 2 x ^{2} + 3 )}

integral from 2 to 3 of 1/(x^2-4x)

\int_{2}^{3} \frac{1}{x ^{2} - 4 x} d x

derivative of 3x^4-5x+2\sqrt[3]{x}derivative of

derivative of ln(1-6x)

\frac{d}{d x} (ln (1 - 6 x))

Frequently Asked Questions (FAQ)

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