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Popular >

derivative of ln(x+y-1)

Solution

\frac{d}{d x} (ln (x + y - 1))

Solution

\frac{\frac{d y}{d x} + 1}{x + y - 1}

Solution steps

\frac{d}{d x} (ln (x + y - 1))

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{\frac{d y}{d x} + 1}{x + y - 1}

Popular Examples

x^2((dy)/(dx))=y-yx

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

normal of y=x^2-6x,(5,-5)normal of

y = x^{2} - 6 x, (5, - 5)

y^{''}-2y^'+10y=9etcsc(3t)

y^{^{''}} - 2 y^{^{'}} + 10 y = 9 e t csc (3 t)

derivative of y=ln(xsqrt(x^2-9))derivative of

y = ln (x x^{2} - 9)

sum from n=1 to infinity of ln(n/(2n+1))

n = 1 \sum \infty ln (\frac{n}{2 n + 1})

Frequently Asked Questions (FAQ)

What is the derivative of ln(x+y-1) ?
The derivative of ln(x+y-1) is (\frac{dy)/(dx)+1}{x+y-1}
What is the first derivative of ln(x+y-1) ?
The first derivative of ln(x+y-1) is (\frac{dy)/(dx)+1}{x+y-1}