What is the derivative of ((5x+3)/(3e^x)) ?

The derivative of ((5x+3)/(3e^x)) is (-5x+2)/(3e^x)

What is the first derivative of ((5x+3)/(3e^x)) ?

The first derivative of ((5x+3)/(3e^x)) is (-5x+2)/(3e^x)

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

\frac{- 5 x + 2}{3 e ^{x}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{3} \frac{d}{d x} (\frac{5 x + 3}{e ^{x}})

Apply the Quotient Rule:

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

= \frac{1}{3} \cdot \frac{\frac{d}{d x} ( 5 x + 3 ) e ^{x} - \frac{d}{d x} ( e ^{x} ) ( 5 x + 3 )}{( e ^{x} ) ^{2}}

\frac{d}{d x} (5 x + 3) = 5

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

= \frac{1}{3} \cdot \frac{5 e ^{x} - e ^{x} ( 5 x + 3 )}{( e ^{x} ) ^{2}}

Simplify

\frac{1}{3} \cdot \frac{5 e ^{x} - e ^{x} ( 5 x + 3 )}{( e ^{x} ) ^{2}} : \frac{- 5 x + 2}{3 e ^{x}}

= \frac{- 5 x + 2}{3 e ^{x}}

\int sin (x) sec^{5} (x) d x

f (x) = x^{2} - 9, at x = 2

\frac{8}{x ^{3}}

\frac{d}{d x} ((5 x^{3})^{x})

x \frac{d y}{d x} + y = 3 x y

What is the derivative of ((5x+3)/(3e^x)) ?
The derivative of ((5x+3)/(3e^x)) is (-5x+2)/(3e^x)
What is the first derivative of ((5x+3)/(3e^x)) ?
The first derivative of ((5x+3)/(3e^x)) is (-5x+2)/(3e^x)