What is the derivative of (3x^6)/(cos(x)e^x) ?

The derivative of (3x^6)/(cos(x)e^x) is (3x^5(6cos(x)-x(cos(x)-sin(x))))/(e^xcos^2(x))

What is the first derivative of (3x^6)/(cos(x)e^x) ?

The first derivative of (3x^6)/(cos(x)e^x) is (3x^5(6cos(x)-x(cos(x)-sin(x))))/(e^xcos^2(x))

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derivative of

\frac{3 x ^{6}}{cos ( x ) e ^{x}}

\frac{3 x ^{5} ( 6 cos ( x ) - x ( cos ( x ) - sin ( x ) ) )}{e ^{x} cos ^{2} ( x )}

Solution steps

\frac{d}{d x} (\frac{3 x ^{6}}{cos ( x ) e ^{x}})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{x ^{6}}{cos ( x ) e ^{x}})

Apply the Quotient Rule:

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

= 3 \cdot \frac{\frac{d}{d x} ( x ^{6} ) cos ( x ) e ^{x} - \frac{d}{d x} ( cos ( x ) e ^{x} ) x ^{6}}{( cos ( x ) e ^{x} ) ^{2}}

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

= 3 \cdot \frac{6 x ^{5} cos ( x ) e ^{x} - ( - e ^{x} sin ( x ) + e ^{x} cos ( x ) ) x ^{6}}{( cos ( x ) e ^{x} ) ^{2}}

Simplify

3 \cdot \frac{6 x ^{5} cos ( x ) e ^{x} - ( - e ^{x} sin ( x ) + e ^{x} cos ( x ) ) x ^{6}}{( cos ( x ) e ^{x} ) ^{2}} : \frac{3 x ^{5} ( 6 cos ( x ) - x ( cos ( x ) - sin ( x ) ) )}{e ^{x} cos ^{2} ( x )}

= \frac{3 x ^{5} ( 6 cos ( x ) - x ( cos ( x ) - sin ( x ) ) )}{e ^{x} cos ^{2} ( x )}

x^{2}, \frac{1}{2} x^{2}, 3 x

f (x) = x^{2} - 3, (- 2, 1)

\int \frac{1}{x ^{\frac{1}{2}} - 4} d x

\int x^{2} 5 - 2 x^{3} d x

\int (x^{1.8} + 11 x^{4.5}) d x

What is the derivative of (3x^6)/(cos(x)e^x) ?
The derivative of (3x^6)/(cos(x)e^x) is (3x^5(6cos(x)-x(cos(x)-sin(x))))/(e^xcos^2(x))
What is the first derivative of (3x^6)/(cos(x)e^x) ?
The first derivative of (3x^6)/(cos(x)e^x) is (3x^5(6cos(x)-x(cos(x)-sin(x))))/(e^xcos^2(x))