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Popular >

derivative of (e^x/(2x^2+5))

Solution

\frac{d}{d x} (\frac{e ^{x}}{2 x ^{2} + 5})

Solution

\frac{e ^{x} ( 2 x ^{2} + 5 ) - 4 x e ^{x}}{( 2 x ^{2} + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{2 x ^{2} + 5})

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} + 5 ) - \frac{d}{d x} ( 2 x ^{2} + 5 ) e ^{x}}{( 2 x ^{2} + 5 ) ^{2}}

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

\frac{d}{d x} (2 x^{2} + 5) = 4 x

= \frac{e ^{x} ( 2 x ^{2} + 5 ) - 4 x e ^{x}}{( 2 x ^{2} + 5 ) ^{2}}

Popular Examples

integral from-1 to 1 of 2

\int_{- 1}^{1} 2 d x

limit as b approaches 0 of b/(x^2+b^2)

b \to 0 lim (\frac{b}{x ^{2} + b ^{2}})

sum from n=3 to infinity of (4^n+1)/(n!)

n = 3 \sum \infty \frac{4 ^{n} + 1}{n !}

derivative of y= 1/((1+x^2))derivative of

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

simplify 3x^{-2}-4x simplify

3 x^{- 2} - 4 x

Frequently Asked Questions (FAQ)

What is the derivative of (e^x/(2x^2+5)) ?
The derivative of (e^x/(2x^2+5)) is (e^x(2x^2+5)-4xe^x)/((2x^2+5)^2)
What is the first derivative of (e^x/(2x^2+5)) ?
The first derivative of (e^x/(2x^2+5)) is (e^x(2x^2+5)-4xe^x)/((2x^2+5)^2)