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Popular >

derivative of ln(xy^2)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

y^{''}+4y=2sin(2x)

y^{^{''}} + 4 y = 2 sin (2 x)

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

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

derivative of 1/(6x^2)

\frac{d}{d x} (\frac{1}{6 x ^{2}})

integral of 1/((x^2-4x+4)(x^2-5x+6))

\int \frac{1}{( x ^{2} - 4 x + 4 ) ( x ^{2} - 5 x + 6 )} d x

integral of 1/(3+sqrt(2x))

\int \frac{1}{3 + 2 x} d x

Frequently Asked Questions (FAQ)

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