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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

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

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

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

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

Popular Examples

y^{''}-4y^'+4=0

y^{^{''}} - 4 y^{^{'}} + 4 = 0

sum from n=0 to infinity of ((3^n))/(n!)

n = 0 \sum \infty \frac{( 3 ^{n} )}{n !}

(\partial)/(\partial x)(xy^2-e^{xy})

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

y^{''}+20y^'+200y=300,y(0)=0,y^'(0)=0

y^{^{''}} + 20 y^{^{'}} + 200 y = 300, y (0) = 0, y^{^{'}} (0) = 0

tangent of f(x)=9+8x+6xe^x,\at x=0 tangent of

f (x) = 9 + 8 x + 6 x e^{x}, at x = 0

Frequently Asked Questions (FAQ)

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