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Popular >

derivative of ln(2x^2y)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

\frac{1}{2 x ^{2} y} \frac{d}{d x} (2 x^{2} y)

= \frac{1}{2 x ^{2} y} \frac{d}{d x} (2 x^{2} y)

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

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

Simplify

\frac{1}{2 x ^{2} y} \cdot 2 (2 x y + \frac{d y}{d x} x^{2}) : \frac{2 y + x \frac{d y}{d x}}{x y}

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

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Frequently Asked Questions (FAQ)

What is the derivative of ln(2x^2y) ?
The derivative of ln(2x^2y) is (2y+x\frac{dy)/(dx)}{xy}
What is the first derivative of ln(2x^2y) ?
The first derivative of ln(2x^2y) is (2y+x\frac{dy)/(dx)}{xy}