What is the derivative of (4x^5)/(e^{3x)} ?

The derivative of (4x^5)/(e^{3x)} is (4x^4(5-3x))/(e^{3x)}

What is the first derivative of (4x^5)/(e^{3x)} ?

The first derivative of (4x^5)/(e^{3x)} is (4x^4(5-3x))/(e^{3x)}

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derivative of

\frac{4 x ^{5}}{e ^{3 x}}

\frac{4 x ^{4} ( 5 - 3 x )}{e ^{3 x}}

Solution steps

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

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{x ^{5}}{e ^{3 x}})

Apply the Quotient Rule:

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

= 4 \cdot \frac{\frac{d}{d x} ( x ^{5} ) e ^{3 x} - \frac{d}{d x} ( e ^{3 x} ) x ^{5}}{( e ^{3 x} ) ^{2}}

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

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

= 4 \cdot \frac{5 x ^{4} e ^{3 x} - e ^{3 x} \cdot 3 x ^{5}}{( e ^{3 x} ) ^{2}}

Simplify

4 \cdot \frac{5 x ^{4} e ^{3 x} - e ^{3 x} \cdot 3 x ^{5}}{( e ^{3 x} ) ^{2}} : \frac{4 x ^{4} ( 5 - 3 x )}{e ^{3 x}}

= \frac{4 x ^{4} ( 5 - 3 x )}{e ^{3 x}}

x \to 0 - lim (\frac{e ^{x}}{1 - e ^{x}})

f (x) = e^{- x} x - 2 e^{- x}

\frac{\partial}{\partial x} (cos (8 x y))

y = 2 x + 8

\int 1 + 36 x d x

What is the derivative of (4x^5)/(e^{3x)} ?
The derivative of (4x^5)/(e^{3x)} is (4x^4(5-3x))/(e^{3x)}
What is the first derivative of (4x^5)/(e^{3x)} ?
The first derivative of (4x^5)/(e^{3x)} is (4x^4(5-3x))/(e^{3x)}