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Popular >

derivative of xy^'

Solution

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

Solution

y^{'} +' x \frac{d y}{d x} y^{' - 1}

Solution steps

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

Apply the Product Rule:

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

f = x, g = y^{^{'}}

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

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

\frac{d}{d x} (y^{^{'}}) =^{'} \frac{d y}{d x} y^{^{'} - 1}

= 1 \cdot y^{^{^{'}}} +^{^{'}} \frac{d y}{d x} y^{^{^{'}} - 1} x

Simplify

= y^{^{^{'}}} +^{^{'}} x \frac{d y}{d x} y^{^{^{'}} - 1}

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\int_{0}^{2} 2 sec (\frac{π x}{6}) d x

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\int \frac{1}{θ ^{2}} sin (\frac{1}{θ}) cos (\frac{1}{θ}) d θ

\frac{d}{d t} (e^{5 t})

Frequently Asked Questions (FAQ)

What is the derivative of xy^' ?
The derivative of xy^' is y^'+'x(dy)/(dx)y^{'-1}
What is the first derivative of xy^' ?
The first derivative of xy^' is y^'+'x(dy)/(dx)y^{'-1}