What is the derivative of (2x^4)/(cos(x)e^x) ?

The derivative of (2x^4)/(cos(x)e^x) is (2x^3(4cos(x)-x(cos(x)-sin(x))))/(e^xcos^2(x))

What is the first derivative of (2x^4)/(cos(x)e^x) ?

The first derivative of (2x^4)/(cos(x)e^x) is (2x^3(4cos(x)-x(cos(x)-sin(x))))/(e^xcos^2(x))

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derivative of

\frac{2 x ^{4}}{cos ( x ) e ^{x}}

\frac{2 x ^{3} ( 4 cos ( x ) - x ( cos ( x ) - sin ( x ) ) )}{e ^{x} cos ^{2} ( x )}

Solution steps

\frac{d}{d x} (\frac{2 x ^{4}}{cos ( x ) e ^{x}})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{x ^{4}}{cos ( x ) e ^{x}})

Apply the Quotient Rule:

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

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

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

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

= 2 \cdot \frac{4 x ^{3} cos ( x ) e ^{x} - ( - e ^{x} sin ( x ) + e ^{x} cos ( x ) ) x ^{4}}{( cos ( x ) e ^{x} ) ^{2}}

Simplify

2 \cdot \frac{4 x ^{3} cos ( x ) e ^{x} - ( - e ^{x} sin ( x ) + e ^{x} cos ( x ) ) x ^{4}}{( cos ( x ) e ^{x} ) ^{2}} : \frac{2 x ^{3} ( 4 cos ( x ) - x ( cos ( x ) - sin ( x ) ) )}{e ^{x} cos ^{2} ( x )}

= \frac{2 x ^{3} ( 4 cos ( x ) - x ( cos ( x ) - sin ( x ) ) )}{e ^{x} cos ^{2} ( x )}

x \to 3 + lim (\frac{∣ x - 3 ∣}{x - 3})

\int \frac{1}{1 - sin ( x )} d x

x \to 0 lim (\frac{sin ( 2 ) ( x )}{x})

\frac{1}{u ^{2}}

\frac{( 6 + 7 x )}{( x ^{4} + 5 x - 5 )}

What is the derivative of (2x^4)/(cos(x)e^x) ?
The derivative of (2x^4)/(cos(x)e^x) is (2x^3(4cos(x)-x(cos(x)-sin(x))))/(e^xcos^2(x))
What is the first derivative of (2x^4)/(cos(x)e^x) ?
The first derivative of (2x^4)/(cos(x)e^x) is (2x^3(4cos(x)-x(cos(x)-sin(x))))/(e^xcos^2(x))