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Popular >

derivative of ln(2x+3y)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(2x^2y+2y+5)dx+(2x^3+2x)dy=0

(2 x^{2} y + 2 y + 5) d x + (2 x^{3} + 2 x) d y = 0

integral of e^{-ax}x

\int e^{- a x} x d x

integral from 0 to 1 of (-5x)/(e^{2x)}

\int_{0}^{1} \frac{- 5 x}{e ^{2 x}} d x

derivative of 16(x+2^3)

\frac{d}{d x} (16 (x + 2)^{3})

laplacetransform 2/5 laplace transform

\frac{2}{5}

Frequently Asked Questions (FAQ)

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