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

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

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

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

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\frac{d}{d x} (\frac{cos ( x ^{3} )}{e ^{x}})

- \frac{3 x ^{2} sin ( x ^{3} ) + cos ( x ^{3} )}{e ^{x}}

Solution steps

\frac{d}{d x} (\frac{cos ( x ^{3} )}{e ^{x}})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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