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Popular >

derivative of (e^x/(2x^2+9))

Solution

\frac{d}{d x} (\frac{e ^{x}}{2 x ^{2} + 9})

Solution

\frac{e ^{x} ( 2 x ^{2} + 9 ) - 4 x e ^{x}}{( 2 x ^{2} + 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{2 x ^{2} + 9})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( 2 x ^{2} + 9 ) - \frac{d}{d x} ( 2 x ^{2} + 9 ) e ^{x}}{( 2 x ^{2} + 9 ) ^{2}}

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

\frac{d}{d x} (2 x^{2} + 9) = 4 x

= \frac{e ^{x} ( 2 x ^{2} + 9 ) - 4 x e ^{x}}{( 2 x ^{2} + 9 ) ^{2}}

Popular Examples

x \cdot y \cdot y^{^{'}} = 1 - x^{2}

derivative of (x^3-x/x)

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

derivative of 4/((x^3+9^5))

\frac{d}{d x} (\frac{4}{( x ^{3} + 9 ) ^{5}})

(dx)/(dt)+2t^5x^7+x/t =0

\frac{d x}{d t} + 2 t^{5} x^{7} + \frac{x}{t} = 0

sum from n=0 to infinity of e^{-6n}

n = 0 \sum \infty e^{- 6 n}

Frequently Asked Questions (FAQ)

What is the derivative of (e^x/(2x^2+9)) ?
The derivative of (e^x/(2x^2+9)) is (e^x(2x^2+9)-4xe^x)/((2x^2+9)^2)
What is the first derivative of (e^x/(2x^2+9)) ?
The first derivative of (e^x/(2x^2+9)) is (e^x(2x^2+9)-4xe^x)/((2x^2+9)^2)