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Popular >

derivative of (e^x/(x^2+7))

Solution

\frac{d}{d x} (\frac{e ^{x}}{x ^{2} + 7})

Solution

\frac{e ^{x} ( x ^{2} + 7 ) - 2 x e ^{x}}{( x ^{2} + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{x ^{2} + 7})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( x ^{2} + 7 ) - \frac{d}{d x} ( x ^{2} + 7 ) e ^{x}}{( x ^{2} + 7 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 7) = 2 x

= \frac{e ^{x} ( x ^{2} + 7 ) - 2 x e ^{x}}{( x ^{2} + 7 ) ^{2}}

Popular Examples

integral of (sqrt(x))/(1+\sqrt[3]{x)}

integral from 1 to infinity of 5/(2x)

\int_{1}^{\infty} \frac{5}{2 x} d x

2yy^'+3-(y^2+3)=0,y(0)=6

2 y y^{^{'}} + 3 - (y^{2} + 3) = 0, y (0) = 6

f (x) = \frac{3}{3 x + 4}

integral from 1 to 2 of (y+5y^7)/(y^3)

\int_{1}^{2} \frac{y + 5 y ^{7}}{y ^{3}} d y

Frequently Asked Questions (FAQ)

What is the derivative of (e^x/(x^2+7)) ?
The derivative of (e^x/(x^2+7)) is (e^x(x^2+7)-2xe^x)/((x^2+7)^2)
What is the first derivative of (e^x/(x^2+7)) ?
The first derivative of (e^x/(x^2+7)) is (e^x(x^2+7)-2xe^x)/((x^2+7)^2)