What is the derivative of (sin(12x)/(e^{7x)}) ?

The derivative of (sin(12x)/(e^{7x)}) is (12cos(12x)-7sin(12x))/(e^{7x)}

What is the first derivative of (sin(12x)/(e^{7x)}) ?

The first derivative of (sin(12x)/(e^{7x)}) is (12cos(12x)-7sin(12x))/(e^{7x)}

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\frac{d}{d x} (\frac{sin ( 12 x )}{e ^{7 x}})

\frac{12 cos ( 12 x ) - 7 sin ( 12 x )}{e ^{7 x}}

Solution steps

\frac{d}{d x} (\frac{sin ( 12 x )}{e ^{7 x}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( sin ( 12 x ) ) e ^{7 x} - \frac{d}{d x} ( e ^{7 x} ) sin ( 12 x )}{( e ^{7 x} ) ^{2}}

\frac{d}{d x} (sin (12 x)) = cos (12 x) \cdot 12

\frac{d}{d x} (e^{7 x}) = e^{7 x} \cdot 7

= \frac{cos ( 12 x ) \cdot 12 e ^{7 x} - e ^{7 x} \cdot 7 sin ( 12 x )}{( e ^{7 x} ) ^{2}}

Simplify

\frac{cos ( 12 x ) \cdot 12 e ^{7 x} - e ^{7 x} \cdot 7 sin ( 12 x )}{( e ^{7 x} ) ^{2}} : \frac{12 cos ( 12 x ) - 7 sin ( 12 x )}{e ^{7 x}}

= \frac{12 cos ( 12 x ) - 7 sin ( 12 x )}{e ^{7 x}}

\int_{0}^{\frac{π}{6}} 4 sec^{3} (x) d x

\frac{d ^{3}}{d x ^{3}} (\frac{1}{x - 1})

\int 16 tan^{4} (x) sec^{6} (x) d x

\int \frac{1}{sin ^{3} ( x )} d x

What is the derivative of (sin(12x)/(e^{7x)}) ?
The derivative of (sin(12x)/(e^{7x)}) is (12cos(12x)-7sin(12x))/(e^{7x)}
What is the first derivative of (sin(12x)/(e^{7x)}) ?
The first derivative of (sin(12x)/(e^{7x)}) is (12cos(12x)-7sin(12x))/(e^{7x)}