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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Graph

Popular Examples

integral of (10x^2)/(x^4-1)

\int \frac{10 x ^{2}}{x ^{4} - 1} d x

sum from n=5 to infinity of (4/5)^n

n = 5 \sum \infty (\frac{4}{5})^{n}

integral of 4x^3(4+x^4)^{1/3}

\int 4 x^{3} (4 + x^{4})^{\frac{1}{3}} d x

derivative of r/(sqrt(r^2+4))derivative of

\frac{r}{r ^{2} + 4}

x(dy)/(dx)=x^3+4x^3y

x \frac{d y}{d x} = x^{3} + 4 x^{3} y

Frequently Asked Questions (FAQ)

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