What is the derivative of f(x)=(4x)/(9e^{5x)} ?

The derivative of f(x)=(4x)/(9e^{5x)} is (4(1-5x))/(9e^{5x)}

What is the first derivative of f(x)=(4x)/(9e^{5x)} ?

The first derivative of f(x)=(4x)/(9e^{5x)} is (4(1-5x))/(9e^{5x)}

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derivative of

f (x) = \frac{4 x}{9 e ^{5 x}}

\frac{4 ( 1 - 5 x )}{9 e ^{5 x}}

Solution steps

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

Take the constant out:

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

= \frac{4}{9} \frac{d}{d x} (\frac{x}{e ^{5 x}})

Apply the Quotient Rule:

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

= \frac{4}{9} \cdot \frac{\frac{d x}{d x} e ^{5 x} - \frac{d}{d x} ( e ^{5 x} ) x}{( e ^{5 x} ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

= \frac{4}{9} \cdot \frac{1 \cdot e ^{5 x} - e ^{5 x} \cdot 5 x}{( e ^{5 x} ) ^{2}}

Simplify

\frac{4}{9} \cdot \frac{1 \cdot e ^{5 x} - e ^{5 x} \cdot 5 x}{( e ^{5 x} ) ^{2}} : \frac{4 ( 1 - 5 x )}{9 e ^{5 x}}

= \frac{4 ( 1 - 5 x )}{9 e ^{5 x}}

(5, - 2), (- 6, 4)

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What is the derivative of f(x)=(4x)/(9e^{5x)} ?
The derivative of f(x)=(4x)/(9e^{5x)} is (4(1-5x))/(9e^{5x)}
What is the first derivative of f(x)=(4x)/(9e^{5x)} ?
The first derivative of f(x)=(4x)/(9e^{5x)} is (4(1-5x))/(9e^{5x)}