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Popular >

derivative of ln(x^2y)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

Popular Examples

derivative of (6x^2+8x+8/(sqrt(x)))

\frac{d}{d x} (\frac{6 x ^{2} + 8 x + 8}{x})

derivative of 84x^6+12x^3-24x^2

\frac{d}{d x} (84 x^{6} + 12 x^{3} - 24 x^{2})

integral of (1-2x)^4

\int (1 - 2 x)^{4} d x

integral of 1/((4+9x^2))

\int \frac{1}{( 4 + 9 x ^{2} )} d x

x^2y^{''}+3xy^'-4y=0

x^{2} y^{^{''}} + 3 x y^{^{'}} - 4 y = 0

Frequently Asked Questions (FAQ)

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