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Popular >

derivative of y-5ln|y|+xy

Solution

\frac{d}{d x} (y - 5 ln ∣ y ∣ + x y)

Solution

\frac{d y}{d x} - \frac{5 \frac{d y}{d x}}{y} + y + x \frac{d y}{d x}

Solution steps

\frac{d}{d x} (y - 5 ln ∣ y ∣ + x y)

Apply the Sum/Difference Rule:

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

= \frac{d y}{d x} - \frac{d}{d x} (5 ln ∣ y ∣) + \frac{d}{d x} (x y)

\frac{d}{d x} (5 ln ∣ y ∣) = \frac{5 \frac{d y}{d x}}{y}

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

= \frac{d y}{d x} - \frac{5 \frac{d y}{d x}}{y} + y + x \frac{d y}{d x}

Popular Examples

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\int_{1}^{2} \frac{5}{x ^{3} + 4 x} d x

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x \to 0 + lim (\frac{1}{x ^{3}})

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Frequently Asked Questions (FAQ)

What is the derivative of y-5ln|y|+xy ?
The derivative of y-5ln|y|+xy is (dy}{dx}-(5\frac{dy)/(dx))/y+y+x(dy)/(dx)
What is the first derivative of y-5ln|y|+xy ?
The first derivative of y-5ln|y|+xy is (dy}{dx}-(5\frac{dy)/(dx))/y+y+x(dy)/(dx)