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Popular >

derivative of f(x)=(e^x)/(8x^2+3)

Solution

derivative of

f (x) = \frac{e ^{x}}{8 x ^{2} + 3}

Solution

\frac{e ^{x} ( 8 x ^{2} + 3 ) - 16 x e ^{x}}{( 8 x ^{2} + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{8 x ^{2} + 3})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( 8 x ^{2} + 3 ) - \frac{d}{d x} ( 8 x ^{2} + 3 ) e ^{x}}{( 8 x ^{2} + 3 ) ^{2}}

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

\frac{d}{d x} (8 x^{2} + 3) = 16 x

= \frac{e ^{x} ( 8 x ^{2} + 3 ) - 16 x e ^{x}}{( 8 x ^{2} + 3 ) ^{2}}

Popular Examples

sum from n=1 to infinity of (4^n)/(6^n)

n = 1 \sum \infty \frac{4 ^{n}}{6 ^{n}}

integral of (((x)^2-5)^52x)

\int (((x)^{2} - 5)^{5} 2 x) d x

limit as x approaches-1+of ln|x+1|

x \to - 1 + lim (ln ∣ x + 1 ∣)

derivative of x^2e^{(-x/(10)})

\frac{d}{d x} (x^{2} e^{\frac{- x}{10}})

tangent of f(x)= x/(x^2-15),\at x=4 tangent of

f (x) = \frac{x}{x ^{2} - 15}, at x = 4

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(e^x)/(8x^2+3) ?
The derivative of f(x)=(e^x)/(8x^2+3) is (e^x(8x^2+3)-16xe^x)/((8x^2+3)^2)
What is the first derivative of f(x)=(e^x)/(8x^2+3) ?
The first derivative of f(x)=(e^x)/(8x^2+3) is (e^x(8x^2+3)-16xe^x)/((8x^2+3)^2)