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Popular >

derivative of ln(e^x+xe^x)

Solution

derivative of

ln (e^{x} + x e^{x})

Solution

\frac{2 + x}{1 + x}

Solution steps

\frac{d}{d x} (ln (e^{x} + x e^{x}))

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2 + x}{1 + x}

Popular Examples

derivative of (3sqrt(x)+x(2-x^2))

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

integral from 1 to 6 of 8x

\int_{1}^{6} 8 x d x

derivative of (5x)/(1+x^2)derivative of

\frac{5 x}{1 + x ^{2}}

(\partial)/(\partial x)(xy+x)

\frac{\partial}{\partial x} (x y + x)

derivative of-2sin(x+2sin(2x))

\frac{d}{d x} (- 2 sin (x) + 2 sin (2 x))

Frequently Asked Questions (FAQ)

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