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Popular >

derivative of ln(e^x-y)

Solution

\frac{d}{d x} (ln (e^{x} - y))

Solution

\frac{e ^{x} - \frac{d y}{d x}}{e ^{x} - y}

Solution steps

\frac{d}{d x} (ln (e^{x} - y))

Apply the chain rule:

\frac{1}{e ^{x} - y} \frac{d}{d x} (e^{x} - y)

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

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

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

Simplify

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

= \frac{e ^{x} - \frac{d y}{d x}}{e ^{x} - y}

Popular Examples

integral of x^3sqrt(x^2-1)

\int x^{3} x^{2} - 1 d x

derivative of 1/((x^2-1(x^2+3x+3)))

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

integral of sin^3(7x)cos^{-2}(7x)

\int sin^{3} (7 x) cos^{- 2} (7 x) d x

ty^'=2y+3t^3cos(2t),y(pi/4)=0

t y^{^{'}} = 2 y + 3 t^{3} cos (2 t), y (\frac{π}{4}) = 0

derivative of (6x^2+4x+6)/(sqrt(x))derivative of

\frac{6 x ^{2} + 4 x + 6}{x}

Frequently Asked Questions (FAQ)

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