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Popular >

derivative of ln(4xy)

Solution

\frac{d}{d x} (ln (4 x y))

Solution

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

Solution steps

\frac{d}{d x} (ln (4 x y))

Apply the chain rule:

\frac{1}{4 x y} \frac{d}{d x} (4 x y)

= \frac{1}{4 x y} \frac{d}{d x} (4 x y)

\frac{d}{d x} (4 x y) = 4 (y + x \frac{d y}{d x})

= \frac{1}{4 x y} \cdot 4 (y + x \frac{d y}{d x})

Simplify

\frac{1}{4 x y} \cdot 4 (y + x \frac{d y}{d x}) : \frac{y + x \frac{d y}{d x}}{x y}

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

Popular Examples

derivative of (18)/(x^4)derivative of

\frac{18}{x ^{4}}

f(x)= x/((1+x^2))

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

derivative of (x^2-3x+2)^5 derivative of

(x^{2} - 3 x + 2)^{5}

integral of x^{12}e^{x^{13}}

\int x^{12} e^{x^{13}} d x

tangent of f(x)=x^2-9,(-2,-5)tangent of

f (x) = x^{2} - 9, (- 2, - 5)

Frequently Asked Questions (FAQ)

What is the derivative of ln(4xy) ?
The derivative of ln(4xy) is (y+x\frac{dy)/(dx)}{xy}
What is the first derivative of ln(4xy) ?
The first derivative of ln(4xy) is (y+x\frac{dy)/(dx)}{xy}