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Popular >

derivative of ln(2e^x-e^{2x})

Solution

derivative of

ln (2 e^{x} - e^{2 x})

Solution

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

Solution steps

\frac{d}{d x} (ln (2 e^{x} - e^{2 x}))

Apply the chain rule:

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

= \frac{1}{2 e ^{x} - e ^{2 x}} \frac{d}{d x} (2 e^{x} - e^{2 x})

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

= \frac{1}{2 e ^{x} - e ^{2 x}} (2 e^{x} - e^{2 x} \cdot 2)

Simplify

\frac{1}{2 e ^{x} - e ^{2 x}} (2 e^{x} - e^{2 x} \cdot 2) : \frac{2 ( - e ^{x} + 1 )}{2 - e ^{x}}

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

Popular Examples

integral of (x^8)/((2-x^9)^2)

\int \frac{x ^{8}}{( 2 - x ^{9} ) ^{2}} d x

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

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

sqrt(y)dx+(x-1)dy=0,y(2)=9

y d x + (x - 1) d y = 0, y (2) = 9

derivative of y=(x^2+8x+3)/(sqrt(x))derivative of

y = \frac{x ^{2} + 8 x + 3}{x}

derivative of ({g}(x(sqrt(x)))/(ax^2+x))

\frac{d}{d x} (\frac{g ( x ) ( x )}{a x ^{2} + x})

Frequently Asked Questions (FAQ)

What is the derivative of ln(2e^x-e^{2x}) ?
The derivative of ln(2e^x-e^{2x}) is (2(-e^x+1))/(2-e^x)
What is the first derivative of ln(2e^x-e^{2x}) ?
The first derivative of ln(2e^x-e^{2x}) is (2(-e^x+1))/(2-e^x)