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Popular >

derivative of y=(e^x)/(1+x)

Solution

derivative of

y = \frac{e ^{x}}{1 + x}

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

Popular Examples

integral from 0 to pi/2 of 15sin^2(2x)

\int_{0}^{\frac{π}{2}} 15 sin^{2} (2 x) d x

derivative of tan^2(6x)derivative of

tan^{2} (6 x)

integral from 1 to 3 of (x^2+3)/(4x-x^2)

\int_{1}^{3} \frac{x ^{2} + 3}{4 x - x ^{2}} d x

(\partial)/(\partial y)(sqrt(38-x^2-4y^2))

\frac{\partial}{\partial y} (38 - x^{2} - 4 y^{2})

x^4+y^3sqrt(x^5+4)(dy)/(dx)=0,y(1)=0

x^{4} + y^{3} x^{5} + 4 \frac{d y}{d x} = 0, y (1) = 0

Frequently Asked Questions (FAQ)

What is the derivative of y=(e^x)/(1+x) ?
The derivative of y=(e^x)/(1+x) is (e^xx)/((1+x)^2)
What is the first derivative of y=(e^x)/(1+x) ?
The first derivative of y=(e^x)/(1+x) is (e^xx)/((1+x)^2)