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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

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

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

Simplify

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

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

y = x^{2}, y = 6 - x

\frac{d}{d x} (ln (e^{x} - 1))

f (x) = \frac{1}{x}, at x = a

\frac{d}{d p} (\frac{p - 1}{p ^{2} + 4})

\int \frac{e ^{x}}{1 + e ^{x} + e ^{2 x}} d x

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