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Popular Calculus >

derivative of ln(3x+2y)

Solution

\frac{d}{d x} (ln (3 x + 2 y))

Solution

\frac{3 + 2 \frac{d y}{d x}}{3 x + 2 y}

Solution steps

\frac{d}{d x} (ln (3 x + 2 y))

Apply the chain rule:

\frac{1}{3 x + 2 y} \frac{d}{d x} (3 x + 2 y)

= \frac{1}{3 x + 2 y} \frac{d}{d x} (3 x + 2 y)

\frac{d}{d x} (3 x + 2 y) = 3 + 2 \frac{d y}{d x}

= \frac{1}{3 x + 2 y} (3 + 2 \frac{d y}{d x})

Simplify

\frac{1}{3 x + 2 y} (3 + 2 \frac{d y}{d x}) : \frac{3 + 2 \frac{d y}{d x}}{3 x + 2 y}

= \frac{3 + 2 \frac{d y}{d x}}{3 x + 2 y}

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y^{''}+7y^'+23y=0

y^{^{''}} + 7 y^{^{'}} + 23 y = 0

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x \to 2 lim (\frac{x ^{2} + 1}{x - 1})

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\int \frac{2 z - 3}{7 z - 10} d z

(\partial)/(\partial x)(2sin(x)cos(y))

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derivative of x/(x^{-1+1})

\frac{d}{d x} (\frac{x}{x ^{- 1} + 1})

Frequently Asked Questions (FAQ)

What is the derivative of ln(3x+2y) ?
The derivative of ln(3x+2y) is (3+2\frac{dy)/(dx)}{3x+2y}
What is the first derivative of ln(3x+2y) ?
The first derivative of ln(3x+2y) is (3+2\frac{dy)/(dx)}{3x+2y}