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Popular >

derivative of ln(x^2y^2)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of \sqrt[3]{x^2}+2sqrt(x^5)

limit as x approaches infinity of (3x^2+10x-7)/(2x^2-5x)

x \to \infty lim (\frac{3 x ^{2} + 10 x - 7}{2 x ^{2} - 5 x})

y^{''}-6y^'+25y=-45cos(2t)+30sin(2t)

y^{^{''}} - 6 y^{^{'}} + 25 y = - 45 cos (2 t) + 30 sin (2 t)

derivative of ln(coth(x))

\frac{d}{d x} (ln (coth (x)))

integral of (cos(5x))/(e^{sin(5x))}

\int \frac{cos ( 5 x )}{e ^{s i n (5 x)}} d x

Frequently Asked Questions (FAQ)

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